Lektion08.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lektion 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrixplots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "i = Symbol('i')\n",
    "j = Symbol('j')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAE4AAAAuBAMAAAB0cDJ0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWa7iUQi\n3TLmasmYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVQ4EWNgIB8IGRCjl9nVnyh1DAz5o+qw\nBugAhUuIfkkDVveMClIQAv+JAxTYMNi0eqI7CEe54YGurgVNgFEZWUAMmQNmQ0VMQj4jS+FUx8BG\nijrm1ASIqTDzmNMmQK2BiYDN4+JWQFXHyqCBTd1B1gJUdT0MH7GpM+BPAAovLy+/VF5eAlJgwP0H\nRCGJQPwhDy09Ya5h4LoAUgcEMBGIuhJmVFEG9gCIAKo65o9caOrsBbCp4/5wAk0dzCGo5jF4NKCp\ni4UaB1PH6vQdOQnAXM1wFU0djAulbSD0Y55/MAmoCIyLQvP84oR5F0Ucg+MWgSEEEgAAWlNZxh0d\nMcAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{1}{i + j + 1}$$"
      ],
      "text/plain": [
       "    1    \n",
       "─────────\n",
       "i + j + 1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def hilbert_element(i,j):\n",
    "    return 1/(i+j+1)\n",
    "\n",
    "hilbert_element(i,j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hilbert = Matrix(20, 20, hilbert_element)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# plt.imshow(hilbert)  # TypeError"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RkSS11CSLmCy5pUKV5SCjZDCSpJaaZILjBiNJUp2mmGCy5K/xqRH1pSqDkSS11GDTdM0M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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xadae662c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.array(hilbert).astype(float), interpolation='none')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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F40YmfX8n8LbU/isHL0mzKGZR45mG8yQdQJHbvwk4leKa17ryuDOAG6mYw29m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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xac2d0d0c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log(np.array(hilbert).astype(float)), \n",
    "           interpolation='none')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hilbert = Matrix(60, 60, hilbert_element)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jas3IayNwD/CzA25/DfAGQJ3PD5Tt0MXLzCxZzU8PJels4EXALwEv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\nuHiZmVly/j8sZtC3wjCBZQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xabefd66c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log(np.array(hilbert).astype(float)), \n",
    "           interpolation='none')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "inv_hilbert = hilbert**(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/braun/miniconda3/envs/compana16/lib/python3.5/site-packages/ipykernel/__main__.py:1: RuntimeWarning: invalid value encountered in log\n",
      "  if __name__ == '__main__':\n"
     ]
    },
    {
     "data": {
      "image/png": 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mdqWZvWBm7WY2ocvr7Wa2ovrf2sd/12hu6vLaCjP7UdHTK80KasdvOTasptTRjDqlji4N\nDBH7BsaJ599KdUE/p8gQEZkhAD7tv0pis+1zSexQPyuJnW9Tk9jJ/rUkdqKdEY59vu+fxA6zGUns\nCk97TO1jaS+qqFzLuKAsEcDDvnUSG2NPJrGorMw2QVmZaJN602CDGuKN73Ujo0OwkW7RRnqmeQEK\nmA1uCnS7B7rrA924OmPPCbR7Bcf8baD7VM91hY6ZO8ci531roN21ATNGpsEC4jJLWwVllqLv+S4D\nOvd/WtvmQR+UOuqlarHrA/cB/wv8Oni9q3Pkk8BPgV/WxBz4CfAtoOMXdGHnSGkSlBBCiIL0xCTR\njd7drwGuATCz5K9/d3+59rmZTQJudPeuhQvfdPe062cBdIlPCCFEjzCzTVm1gurKFDN7xcweMLNT\nzWzdosfXCkoIIVqVntyo29xlyQHAYuA3XeKXAM8ALwL/CpwObAt8vsjBlaCEEKJV6WYPauZrMLPL\nNvCi5rr4DgQudveltUF3r11RPWRmLwHXm9l73P2p3IOXJkHdfVKXShLn1akk8ZXAEPF4eufZ8pHp\navK9nlY6yO3nBLEh4nCfnsTOtaOSWGSIOC4wRFzgU8KxD7ZL0vn4Hklskt2QxO7yUUlsrN2fxKKq\nDwDbB5UfXvP1k9hmtiSJRRvPQ4KN52gzG+oYHXI3yHM33INNfIg38n1WcMyJge7yQLdPoJtZZ+y2\nQHtxcMz9mqtr+Ji55/3rOmN/tgEzRu7nXaSKRdDLarOgl9XL/g+dni/0PvJyd7MH1Ta88qhl3hIY\n80DjQ5vZWCqron0y5HdRMUuMBFovQQkhhCjImr3E93+Aue7BX/4pH6Li7HupyABKUEII0ar0gs3c\nzNanstLpuFy1tZmNAha6+3NVzQZU9pOODN6/NfBF4HfAa8AoYDrwh8xktpLCubS7m7iqmhPN7EUz\ne9PMrjOzkUXHEUIIsUbYAbgXmEtl1fM9YB7w7RrNvtX//iJ4/1JgT2AO8DBwBnA5kOSK7ujJCmq1\nN3GZ2dHAEcD+wNPAycAcM9u+60aaEEKIBuiFFZS7/4FuFi/ufj5wfp3Xngd2LzirkMIJqrubuICp\nwEnufnVVsz+wAJgEXFbvuDv+xLF/qqkkcXydShL3BJUkdkh/lu/2x5LYM5a2iMhtlwFxhYjIEHGa\np7HjLDVTXOSTk9hBFv1BAtf6R5LYePtDErvPt0tiO9kjSex53ySJbWPxPXVR5YdhQeWHaEN5QLCh\n3CvVHHI30oPN+WhjHmIDQ2heuDDQHRDozgt0X6kz9jmB9vDgmGcFuqk91xU6Zu4cfxrovlxn7Fwz\nRubnmPu9gAItRYL2LJu+u7MpYqO+qiTRCzfqlommOuLN7D1UymBc3xFz98XAncAuzRxLCCHe8fRC\nLb4y0excOoLKNcsFXeILSOs3CSGEaITeqcVXGkqz2PNrjsLXWdVVdeJcY/LkybS1ta3BWQkhxOqZ\nOcu59Ped9/8XLUo7QfcKSlCFmE/Fmjiczquo4VRcIXWxT0zH/mn0yuez6uxBCSFEmWibaEz5rys7\nxebNm8eYMX2wB9XPaWqCcvenzGw+MA74E6z0y+8MnLO69959SJdKEr+vU0lizzRxbbL8+ST2yqBt\nk9genraduCEwRBzsPwzHzm2ZkWuI+FJgiIjMEAAfDwwRD/p7k9gH7S9JLGoPsHnQBmPp6/HXYcjQ\nBtpb5G48F6nmkLtBnrvhHpgXIDYwZBsITg90Xw90p9YZ+5uB9sTgmMc3V9fwMXPP+3t1xv7vnptL\nsj/voBoI1KkIklud4tnOGzv+Uvz7q+l07CsVfU+LUDhBZdzEdSZwnJk9TsVmfhLwPDCrKTMWQghR\nQZf4EnYAbqRihui4iQvgIuAgdz/dzNYDzgOGArcA43UPlBBCNBklqM5k3sQ1DZjWsykJIYTIQpf4\nhBBClBKtoPqGHa9y7IGaShJfil1867/+WhJbMnTzJLarX5/EbrXxSexA/3ES+5kdEY6d2zIj1xBx\nve+axD5ut4ZjR4aI9weGiJd9wyS2maWW16gNxuCgDQaAPxxsFG/fwIbybwPdpxqs5pBZraBQRYXA\nwBCaF6YFummB7rhAd3Kdsb8WaM8IjtlkXaFjfiPQfafB8841YwQmi9BgUaSKRW6rkOB7PmBs55Y/\n9mofVZLo55QmQQkhhCiIVlBCCCFKiRKUEEKIUiKThBBCiFLSz1dQLVTXVgghxDuJ0qyg7t67S6mj\nx9tD3fKRw5LYKL8rid1v45LYFL8giV1ihyWx4/3YcOwTA8feBT4liUU9naISRpFjL3LrQezYe83X\nT2Kb2pIk5gsC19HwvD5NEPdq8psCx9PuDZQlCnoqQZ2+SrnlhnJdeIHLDGKnWbbD7auB7geB7rA6\nY/840B4SHPMnzdU1fMzc8z6yztjf77kLMPvzDvpYQZ1eVrku0lu7lDp6tA9LHfXjFVRpEpQQQoiC\naA9KCCFEKdEKSgghRClRghJCCFFKlKD6hh3vcWxxTamj3WOD4db+cBJ70nZKYp/1mUns13ZQEjvW\nT0hip9gp4djn+/5J7GC7JInFhoi8fk6RGQJiQ8SwyBDxQrCp+65gU/feQPehOiVggl5NYZ+m3FIx\nmf19oEB/odxyQ0VK/uRu+OcaCPYPdDPqjD0l0F4SHHPfQHdpz3WFjpk7x4MC3QV1xg5MI6FhJDBZ\nhAaLzO8FFDDfBMaJAV/sUupoPZU6agalSVBCCCEKIpOEEEKIUqJLfEIIIUqJEpQQQohSokt8fcPd\nO3SuJLHR2y+FuoXrbJ/ExvsVSWy2tSWxo/y0JDbdvp3EfuwHhmMfZjPScXyPdD4NGCIiMwT0jSHC\n59S5w36vBu6wD+7aD+/YD6oAQJ1KALl9iHJNDsEmPsQb+dnGgM8Hul8Gukl1xr4i0O4dHPOq5uoa\nPmZwPuG5BEYMqGPGyDSXZBssilQOye07dVmXShJPqpJEM1AtPiGEEKVECUoIIVqVjhVUkUc3Kygz\nG2tmV5rZC2bWbmYTurz+s2q89vG7Lpq1zewcM3vVzP5mZr80s02Lnp4SlBBCtCoDWLUPlfvo/rf+\n+sB9wH8C9a5VzgaGAyOqj657KmcCnwI+B+wG/BPwq9zT6qA0e1BCCCEK0rEqKvqe1eDu1wDXAJiZ\n1ZH93d1fiV4wsw2Ag4DJ7v6HauxA4GEz28k9aD/Rs6n2HTs+145tsOpu7OUjNwt1u/hNSex2m5TE\nDvWzkti5dkwSm+6HJ7Gj7Gfh2Ff4+CQ2yW5IYvf5dknsg4Eh4mXfMIlF7TKggCHi7kC3Y6D7baD7\nVJ077C8OtPs10AajyN39ue0tcqs5ZJocoIDRIddA8LFAd12dsfcItDcEx9wt0N3cc12hY+bOcXyg\nm11n7AZMFqHBIvN7AQXMN4FxYsD/dKkkMW8eHNMHlSTWnElidzNbAPwVuAE4zt0XVl8bU53V9R1i\nd3/UzJ4FdgFaL0EJIYQoyJpJULOpXK57CtgGOA34nZnt4u5O5ZLfUndf3OV9C6qvZaMEJYQQ/ZSZ\nt1YetSx6s7FjuvtlNU8fMrMHgCeA3YEbGzt6Z5SghBCiVekwSdSh7SOVRy3znoAxX2veFNz9KTN7\nFRhJJUHNBwab2QZdVlHDq69lIxefEEK0KkUt5j0xVXSDmW0ODAM6qivMBZYD42o0/wxsCdxe5Nil\nWUHdvcUARo9clS/f6w+Gur/Y7klsil+QxC6xqUnsND8qiR1j5ySxy31iOPY+NjuJ3eWjkthO9kgS\ne8k3SmKb2aIk5gvq3OWeWyGiAUOEX1hn7AMauMM+uGs/vGM/qPoA+ZUfwqoPDZgcoI7RodnmhZ3r\njH1noB0THHNuc3V1tcE8wzn+W6C7Le/nA3V+Rpkmi+zPu0jlkFzjxJldKkk817qVJMxsfSqroQ4H\n39ZmNgpYWH2cQGUPan5V913gMWAOgLsvNrP/Baab2V+BvwFnA38s4uCDEiUoIYQQBenmEl/d96ye\nHahcqvPq43vV+EVU7o36V2B/YCjwIpXEdLy7L6s5xpHACuCXwNpUbOupZboblKCEEEKspHrv0urS\n2CcyjvF34KvVR49RghJCiFalnxeLVYISQohWpRcqSZSJ0kx1tzcXMvCNl1c+XzTk/aHu056Wc7ra\nDkpix/oJSewUm57ELvLJSexLNisc+xbfMYmNtfuT2PO+SRLb3BYmsfbXgjvSh9e5yz23ZUYDhojI\nDAG9YIjIbIsABdpb5FYgKFLNIdfokGtKGBXo7q8z9vsC7UPBMbcLdI/0XFfomLlzLHLeuSaLXLNK\n5vcCCphvAuPEgO8GlSSm90Elid7ZgyoNpUlQQgghCqJLfEIIIUpJP7/E10KLPSGEEO8kWiiXCiGE\n6IQu8QkhhCglMkn0DTevtxGjh6zqCBz1fQK43T6XxP7LT09iZ9u3k9iP/cAkdpj9Iold77uGY4+z\nu5PYE/6uJLaNpX28lr6e/qgHDwscQg/UKcMSOfbmNNex56fXGfvrDZSAyXTsRf19oE6Pn9z+S7lO\nryLlhjIdadlOuK3qjP10njbUbRHonsvT1dXmjj0y0D2e5wCEOi7AXJdkruuySGmrXGffCV1KHb3U\nuqWOykRpEpQQQoiCyCSxCjM7xszuMrPFZrbAzH5jZtsGuhPN7EUze9PMrjOzkc2bshBCCGDVJb4i\njxa6xFd0qmOBHwA7A3sCawHXmtm6HQIzOxo4AjgE2AlYAswxs8FNmbEQQoh3BIUWe+7+ydrnZnYA\n8DKVHvQdfRunAie5+9VVzf5UWv1OAmo7MQohhGgE7UGtlqFUyrEvBDCz91DpOX99h6DaG+ROYBdW\nk6A+5c8w2IesfP5M0PcJYH8/P4nNsK8nsemeVnY/yn6WxK7yjyWxve3WJAbwsG+dxLa3F5LYG2+v\nlcSGDA02Vh8ONmA/UKcMy/WBdq/gmBdnGiKi8kWBGQIKGCIOCXQ/yTNERGYIKNALKLdETpGyOw0Y\nHUIDwWaB7qV47PZNgnI6r6TaXN3SjQKTzsLGxs49n1zTBhQwWeSaVTK/F1DAfBMYJwb8LCh1dH4f\nlDpSgooxMwPOBG519z9XwyOoJKwFXeQLqq8JIYRoFv3cJNHIVH8E/Avw782YyF+POo0BG/7DyucT\nbQiTJ0+mra2tGYcXQoheYeaTzqUTJnSKLVqUdsvuDXwAeMEVkbeQSaJHCcrMfgh8Ehjr7i/VvDSf\nSpvg4XReRQ0H7l3dMf9x+jEMHv2+lc9npeZAIYQoHW1bG1N+dmWn2Lx58xgzpg8u8fVzCufSanKa\nCHzU3Z+tfc3dn6KSpMbV6Deg4vq7rbGpCiGEqGXFQFgxqOCjv+5BmdmPgDZgArDEzIZXX1rk7m9X\n//9M4Dgzexx4GjgJeB6ImyxV+a29m9E1q6bxfkWom20HJ7Hj/dgkdqKdk8Qu94lJbB+7LonN9bgX\n1Rh7Mom95usnsWHrLEti/mSwAbt9sAF7U5273McF2pnBMffLNERE/ZwCMwQ0aIj4fKD7ZV6fJoh7\nNUWVH8KqD7n9ioKNeaizOZ9pDMg1GizZIB57/cWpdtF6qXbDN5ura/SYuWaM6OcDdcwYuSaU3M87\nME5AHVNNrnHi0C6VJF7pm0oS7dUEVfQ9rULRS3yHUjFB3NQlfiAwA8DdTzez9YDzqLj8bgHGu/vS\nxqYqhBCilhUDjeUDreB7nMqv8fJT9D6orEuC7j4NmNaD+QghhMhkxcCBrBhUbKdmxcB2ILbal40W\nMhwKIYSopX3gQFYMLJag2gcarZKgWshwKIQQ4p1EaVZQk/1B1vVVWf1+mxTq4tYapySx833/JHaw\npT6NW3zHJDbWHgzHfsk3SmKb2ZIk5i8EG6tbBxurtwa63evc5X55oG0LjnlWpiHiuLzqENA3hojI\nDAEFDBG5VR8KVDVoxOgQmRxeHZzqNl4ajz1/UKodsTzV5uqeC3RbBLoix8w9n1yDBeSbLLJbimR+\nL6BANZJJwfdiVlBJ4te9bzNfwQBWFCwNsaKX5tIblCZBCSGEKMYKBrJcCUoIIUTZaGcgKwr+Gm/v\nXlIalKCEEKJF6dklvtZJUUpQQgjRolRWUMUSVLsSVHF+Ye9ntI1e+XyyX1RHl9taY0YSm+17JLHx\ndncSe8KcEZh+AAAgAElEQVTfFY69jS1MYu2vBRum7wo2Vu8ONmB3DXS/rnOX+z6B9pzgmFMzDREn\nB7rD6ozdB4YIH1Nn7Lm9b4iINuYh3pzP3fDPNRo8GegAts7URrrHAt22mbp62tyxc80YkcECYpNF\nrgklu/1H8P2BOt+h3YJj3hzovtilksTC1rgRtuzIZi6EEC1Ke/USX5FHeze/9s1srJldaWYvmFm7\nmU2oeW2QmX3XzP5kZm9UNReZ2WZdjnFT9b0djxXVUnmFUIISQogWZTkDWF518uU/uv21vz5wH/Cf\npDWR1gM+CHwb+BDwGeCfSWutOvATKp0sRgCbAenlr24ozSU+IYQQxWhnUA9cfKs3mrv7NcA1sLIx\nbe1ri4G9amNmdgRwp5lt7u7P17z0pru/UmhyXdAKSgghWpTeuMTXA4ZSWTG93iU+xcxeMbMHzOxU\nM1u36IFLs4I6yO9iiP915fNb7Uuh7lg/IYmdkt1a44Ykdp9vl8Q+aC+EY7/x9lpJbMiwYMP0gWBj\ndcdA99tA99k6d7mfF2gPD445reeGCPtxnbH37X1DRGSGgLgVRiNtMHI33CG/UkKuMSDXvADwUKB9\nX6C9P9CNakBXRJs7xyLnnWsuyTWr5H4voEC7jj0CY9SNQSWJOWWtJNG8BGVmawPfAX7u7m/UvHQJ\n8AzwIvCvwOnAtsDnixy/NAlKCCFEc7lm5iKumbm4U+yNRc2pJWFmg4DLqaye/rP2NXf/ac3Th8zs\nJeB6M3tPtbFtFkpQQgjRonRX6mjPto3Ys61zDdFH5r3F/mOeaGjcmuS0BbBHl9VTxF2AASMBJSgh\nhOjv9KzUUWMtdWuS09bAR91r9mbq8yEqK62XioylBCWEEC1Kh/Gh6HtWh5mtT2Wl0+Hg29rMRgEL\nqSSYX1Gxmn8aWMvMhld1C919mZltDXwR+B3wGjAKmA78wd3jVhF1UIISQogWpb0HJokMF98OwI1U\nVjwOfK8av4jK/U97V+P3VeNWff5R4GZgKbAnMJXKPVXPUVlxpX2RuqE0CeoC26lTqaOD/Yeh7nz7\ndhprqPfTI0nsZd8wHHvTdZYlMX8ycP58IHD+XB/oPhXoLqxThuUrgfbU4JjTAt1X8xx7kVsPwC7t\nfcde5NaDxhx7jZQlgtg9lutIy3W43VNn7B0C7R2B9sNN1tXTRvOM5tiIAxDin1GuS7IRZx/UKYuU\n6+zbq0upo8WtW+rI3f/A6m9BWm2Gq94LtXsz5lKaBCWEEKIYa9pm3tsoQQkhRIvSs4aFjZkk+hIl\nKCGEaFHWhIuvL1GCEkKIFkWX+PqIr/qNbODPrnw+244Idaf5UUnsmCb3ftrGFoVj+4Jgw3TrYMP0\njkA3LtDNDHQH1CnDcnqg/WZwzK8Fuh8EuimBLjBDAPj4TEPEzj03RERmCID2TYKyMq/0fIM8d8Md\n8g0RucaAXPMCwC2BdmygvTHQfbQBXRFt7hxzDRaQby7J7U+V+72A/P5hkfFnwLyg1NGY3i911LOG\nha2zgmqdVCqEEOIdRWlWUEIIIYqxotoPquh7WgUlKCGEaFFW9MAkIRefEEKIXqe/70GVJkH9wD7a\nqZLEUX5aqJtu05PYxf6FJLZfA72f3noj/rGsOzzYML032Fj9cKD7daBrC3Rn1bnL/euB9hvBMc8I\ndAcFuksC3d51xp6daYi4M9Bt1/N+TtA3hogiVQ1yN/wbMTlAbEq4NtB+PND9LtB9MlNXT5s7dq7B\nokgVi1wTSiPGCahTdWKr4Pv7dKDbtUsliTf6ppKEXHxCCCFKSX+/Ubd1UqkQQoh3FFpBCSFEi6JK\nEkIIIUqJ9qD6iKP9d/yj/3nl88vsmFB3lh+axKbaZUnsJt8lie2e2Vpj0yF17jSPWmt8KNgwnRPo\nPhvofhroptYZe1qg/U5wzEMC3QWBblKgu6rO2P/WgCHikZ63y4C+MUREZgjIr/yQawzINRoAzAq0\nEwNts3VFtLlmjCLnnWsuabZxAmDJBql2/cV53/MBj6qSRG9QmgQlhBCiGL3UsLA0KEEJIUSLsrwH\nLr6i+jVJ66RSIYQQ7yi0ghJCiBZFLr4+4rv2yU6VJI71E0LdKXZuErvCxyexSXZ7EnvM353Etg1a\na0RtNaBOa41bgw3/vQLdxYHuy4Hu1DpjTwu0Xw2O+ZNA9/lAd0Wg26PO2LcF2vdlGiKiFgaBIaLI\n3f3NNkQUqWqQa4jINRD8ss7Yn8/URrpLA92+mbp62tyxcw0WkXECYvNEs40T0fcH4u9QbrsX/1CX\nShJvqpJEMyhNghJCCFEMufiEEEKUkv7ebqPQTM3sUDO738wWVR+3mdknumhONLMXzexNM7vOzEY2\nd8pCCCHeCRRNpc8BRwOjgTHADcAsM9sewMyOBo4ADgF2ApYAc8xscNNmLIQQAljVD6rYo59e4nP3\n33YJHWdmhwEfBh4GpgInufvVAGa2P7AAmASk5R5q+Jb/hmE+d+XzGfbtUHe+75/EDrbZSewuH5XE\ndrJnktii5esksQ2DthoA/kCw4b9rZmuN/fJaa9g364z9tUD7g+CYUwLdLwPdxwLdDXXGHhVoH8o0\nRDyX6qI79iMzBPSNISIyQ0B+BYRcY0Cu0QDg4kC7X6Bttq6INteMUeS8c80lucaJIpVD5gfaEYE2\n+p4PeF6VJHqDHl+MNLMBZjYZWA+4zczeA4wAru/QuPti4E4grTskhBCiIToqSRR59OtKEmb2fuB2\nYB3gb8Bn3P1RM9sFcCorploWUElcQgghmohs5imPAKOADYHPAzPMbLdGJzL3qMtYa8N1Vz6faFcz\nefJk2traGj20EEL0GjPfdC6dMKFTbNGi9P7K3qC/NywsnKDcfTnwZPXpvWa2E5W9p9MBA4bTeRU1\nHLi3u+OOmf4Fho3ecuXzGXZw0akJIUSf07aeMeXKKzvF5s2bx5g+2IPq7zRjrTcAWNvdnwLmA+M6\nXjCzDYCdgduaMI4QQoga2nvg4uvOJGFmY83sSjN7wczazWxCoFnt7URmtraZnWNmr5rZ38zsl2a2\nadHzK7SCMrNTgdnAs8A/AFOAjwAfr0rOpOLsexx4GjgJeB6Y1d2xT7LPdCp1dLJ/LdQdZzOS2Gzf\nI4mNt/uT2PO+SRLbfNDbScyfrVPy5wOBo+f6zN5P5+X1fvLj6ox9RqA9KDjmJYFu70B3XaDbuc7Y\n9wfakXmOvaUb5fXYiRxU0DeOvSJld3Ide7kOt8gxB7Fr7sJAe0CgOz/QHZypq6fNHTvXAVikxFNf\nOPsg/g7l9iPzbbuUOnq7pUsdrQ/cB/wv8OuuL9bcTrQ/ld/zJ1O5nWh7d19alZ0JjAc+BywGzgF+\nBYwtMteil/g2BS4CNgMWAX8CPu7uNwC4++lmth5wHjAUuAUYXzNpIYQQTaI3bObufg1wDYCZWSBZ\n7e1E1StnBwGT3f0PVc2BwMNmtpO735U716L3QX05QzMNmFbkuEIIIYrT16WO6t1OZGYdtxNdBuxA\nJbfUah41s2ermt5JUEIIIcpDx75S0fc0wAi6v51oOLC0eh9sPU0WSlBCCNFPeWLmPTw5855OsaWL\n0n33slKaBHWSX8rGvsrsd76dEeou9i8ksf3shiR2n2+XxD5orySxpa+nP4LBW9Yp+XNHYAwYF2yY\nzgx0X8nr/WQn1xk76v10QWbvp6sC3W6B7s46Y28XaB/P650zeGGqe3VwXkkZgMf6wBARmSGg+YaI\nXKMB5BsdfhzoDmtAV0SbO8ciZZZyyyLlGieKlLZ6MtBuHWgj48/af11TpY5Wb5LYqm1ntmrbuVPs\ntXnPctWY03o65Hy6v51oPjDYzDbosooaXn0tm9a5pVgIIUQnVvSg1FEje1CZtxPNBZZ30fwzsCWV\nKkTZlGYFJYQQohi94eIzs/WBkVRWSgBbm9koYKG7P0c3txNVTRP/C0w3s79SKYl3NvDHIg4+UIIS\nQoiWpZdcfDsAN1IxQzjwvWr8IuCgzNuJjgRWAL8E1qZiWz+80ERRghJCiJalox9U0fesjuq9S6vN\nYt3dTuTufwe+Wn30mNIkqG/Zvp0qSZzu/xXqvm5pW6nrfdckNs4eSWIv+4ZJbNOhgYHg4ToVFT4c\naGcFBoK2nvd+ivo+QYO9n/YIdDcHuqDvE4A9Emg3C3rivJJ3J/7GS1NdZIYA2DbYpL4nc+P7xgb6\nOUHfGCIiQwI0ZnQ4O9D9V6aunrYvjBOQX3UiMk7kGmCi7w/ADoE2u0fUll0qSSztm0oS/Z3SJCgh\nhBDF6O8NC5WghBCiRVE/KCGEEKVE/aCEEEKUkvYemCR0ia8HfMcvZhO/aeXzc+zsUHe5T0xi+9it\nSexh3zqJbW9pl0tfEBgItq9TUeGmQDsx2DC9MLO1xrRAF7TVAPBDGmitcUOgGxPogrYaAL5VoH0p\n1S7ZIK81wXPBxnNkhgC4P9BGm9mRIeKjDbTLgL4xRNSr5pBrdJge6I5qQFdEmzvHXOMENNauIzJO\n5H4vIL+NS2T8GfrWmqkk0d8pTYISQghRDO1BCSGEKCVy8QkhhCglfd0Pqq9RghJCiBalNypJlInS\nJKhv2H6dKkmc5YeGuqk2K4nd4jsmsbH2ZBJbtHydJLbh8MBA8ECdigq7B9rLAwPBAYHu9EA3LdAF\nbTUA7CdNbq0xN9AFbTUA7Om81hrrL867E3+LYOM52qAGGBVob8nc+I5aMuRWh4C+MUQUqeaQa174\nbqA7OlNXT9sXxglorF1HrgEm+v4AjA20uS04fHiXShLL+qaSRH+/xNc6az0hhBDvKEqzghJCCFGM\n7hoW1ntPq6AEJYQQLcqKHlzi0x6UEEKIXkcuvj5iul/Apj5n1XM7N9T9yj+dxD5ndyexJ/xdSWyb\nQW8nMX82MBB8oE5FhesD7T7Bhul5ge7rge64QBe01QDw/TNba3ys5601orYakN9a49XBea0JotYa\n0R37AHcE2mgzO2q18MnMCgSRGQKab4goUs2hEaNDpDsl0B3b4NjNNk5AftWJ3CofkVEm+l5A3IYj\nqloSfc83WbZmKknIxSeEEKKUyMUnhBBCrAG0ghJCiBZFLj4hhBClZDkDGFgwQS1XghJCCNHbtDOo\nB/2gWufXfmlmepQd1KnU0Q/94FB3hF2dxO7yUUlsJ3shib3x9lpJbMiWgcPt7jolf8YF2pmBG+4r\nge7UQHdyoDusztgzAu2k4JjXBbqd83o/RX2fIL/308ZL80rFRL2fIgcVwIcze/x8vIGeQVEpHWh+\nCaPcskTQmBOvEV09bV84+yB29+W6KRvpEQVxuazcHlFLh3ZelSxb0VeljnSJTwghRAlZwQAG9OP7\noFpnpkIIId5RaAUlhBAtSnv7QFa0F7zEV1C/JlGCEkKIFmXF8gGwrOAlvuWtc+GsNAnqTP8pw/2f\nVj4/w84PdVf4+CQ2ye5PYk/7iCS21TrLkpg/GRgIdqxT8mdOoG0LzAbnBLpvBrqvBbof1xl7SqC9\nIjjmHoHuzkD3vkAX9H2Cxno/Rb1zoo3nqKQM5Pd+inoB5Roiot5CEJfdyTVERJv9uUYDaL4h4tuB\n7oQ+GrtIiadcE0qze0RBXFYrMuk8F+i2XNG51NFafVXqaMVAWFGw1NEKraCEEEL0Mu3LBxZeQbUv\nb50E1TprPSGEEL2OmT1lZu3B4wfV1y8MXvtdb8xFKyghhGhRVrQPwAtesmtv73ZdsgN08q5/ALgW\nuKz63IHZwAGAVWN/LzSJTJSghBCiRVmxfCDtBS/xeTeX+Nz9tdrnZrY38IS731IT/ru7v1Jo4B5Q\nmgT1/9mXO1WS+LEfGOoOs9lJLK4kMT+JvfVGerrrbh0YCO6oU1Fhr0B7cWA2ODzQnRjozgh0h9QZ\n+5JAu3dwzBsC3ZhA91B+JYmo99Oi9fJ6P0WVJKI78aMNasjv/RRtfEeVBaKN9KhSAcR9iKJN/MgQ\nERkDcqtDQGNGh0Z09bS5hohGKk5AbJ5odo+o6PsDcTWS+wPtqEC3ZEjnVclbfVRJwtsH4gVNEhSw\nmZvZWsAU4P92eWl3M1sA/BW4ATjO3RcWm0j3lCZBCSGEKEgPbOYUs5l/BtgQuKgmNhv4FfAUsA1w\nGvA7M9vF3ZuamZWghBCiVVkxsPKox5Uz4epfdI4tfr3ICAcBs9195SUpd7+s5vWHzOwB4Algd+DG\nIgfvjoYSlJl9AzgVONPdj6qJnwh8GRgK/BE4zN0fb2QsIYQQBZnQVnnU8uA8mLhDt281sy2BPYFJ\nq9O5+1Nm9iowkiYnqB7bzM1sR+AQ4P4u8aOBI6qv7QQsAeaY2eAG5imEEKIryw2WFXwst+6PW+Eg\nYAGwWgu5mW0ODANeauxkUnq0gjKzIcDFVFZJ3+ry8lTgJHe/uqrdn8pJTmKVTTEhrSTxs1B3lX8s\nie0dVJJ43jdJYpsPCYwBUSWJD9ep5vDbQLtfcMyzAt3xmZUkflJn7H0D7VXBMXcLdHMD3XaNVZLY\n8M2eV5KINp6jO/Yhv7VGI5UkotYNkF/VILdSQmQgiIwGEJsSmm2IqFdJIlfbbOME5FflyG3BUaSS\nRFS1JDLp5FSSWLePKknQDqzowXu6wcyMio38Qndvr4mvD5xAZQ9qPpVV03eBx4A5BWfSLT1dQZ0D\nXOXuN9QGzew9wAjg+o6Yuy8G7gR26ekkhRBCBCwHlhV8xPm5K3sCWwBdVworgH8FZgGPAucDdwO7\nuXtaS65BCq+gzGwy8EEqN3N1ZQSVm7gWdIkvqL4mhBCiWayg+AoqQ+/u10HaaMrd3wY+UXDEHlMo\nQVWvNZ4J7NnsbHnjUbNZe8N1Vj5/zO5m8uTJtLW1reZdQgixZpnlznUTJnSKLVq0qG8G71hBFX1P\ni1B0BTUG2ASYV71GCZUsu5uZHQFsR6X0xXA6r6KGA/eu7sAfnT6e4aNr96COKzg1IYToeyaa8dUr\nr+wUmzdvHmP6Yg+qn1M0Qf2eSl2mWi4EHga+4+5Pmtl8YBzwJwAz2wDYmcq+VV3yK0lcl8Tm+vuT\n2BhLq3A0XEniU5mVJKb2QiWJSzMrSdycWUnikUC3RfMrSTyWeSd+vUoSUWuN32VufEeVBaJKElGl\nAshvrZFriGjlShLNNk4UqSTR7BYc/amSRG+ZJMpCoQTl7kuAP9fGzGwJ8Jq7P1wNnQkcZ2aPA08D\nJwHPU9lUE0II0Sx0ia9bOv2p4O6nm9l6wHlUbtS9BRjv7kubMJYQQogOeskkURYaTlDuvkcQmwZM\na/TYQgghVoNWUEIIIUqJ9qD6hsYqSTyYxFRJokaXW0niuXjspRvlVZKI7rDfthcqSXwys2JA1Goh\n2kiPWjdA37TWqFdJoi8MEe+EShJRy5WowgjkV5KIWshss6YqSfRzSpOghBBCFESX+IQQQpQSXeIT\nQghRSrSCEkIIUUr6uc28x/2ghBBCiN6kNCsolTqq6kpY6mjwwrxSR1uo1NFKcns/1St11BeOvf5W\n6ij6vCMnZ78qdaRLfEIIIUqJTBJCCCFKiVZQQgghSkk/N0koQQkhRKuiFVTfoFJHVV0JSx21b5JX\n6mi+Sh2tJCrlk2ucgNhsoFJHq8gtdRR9LyJDDeSXOopKem2pUke9QmkSlBBCiILIJCGEEKKU6BKf\nEEKIUiKThBBCiFKiFVTf0Eglibt8VBLbqZFKEnf3s0oSO2dWktgqHnvAK3mVJEZk9s6J7sS/p0Al\niagSQLTxHfUCiipJRBvuEFcriIwTUfWDRowTkF91oq8qSTTbEBGZISA2RESVPiJjS29Ukngo0L4v\n0C0d2rmSxLK+qiSxguIJp4VWUKrFJ4QQopSUZgUlhBCiIP18BaUEJYQQrYoSlBBCiFKiBNU3TPcL\n2NTnrHpep5LEFT4+iU2y+5PY0z4iiW0VVZJ4NjAQ7FinmsOczEoS52RWkvhGgUoSUzIrSewR6O4M\ndO8LdE/XGXuzvEoSrw5OdVtnbjzvUODu/mgzO2rB8fnMjfSoAgHEm/ONtODINU5Avikh1ziRqysy\ndq4hIjrv6OcD+a01ooogkQGmSCWJqOVLVOEkqpiyWZdKEmv1VSWJ5RRPUC3k4pNJQgghWpWOFVSR\nRzcrKDM7wczauzz+3EVzopm9aGZvmtl1ZjayyWcGKEEJIYRIeRAYDoyoPnbteMHMjgaOAA4BdgKW\nAHPMbHCzJ1GaS3xCCCEK0nt7UMvdPb2ZtMJU4CR3vxrAzPYHFgCTgMsKzma1aAUlhBCtSi9c4qvy\nXjN7wcyeMLOLzWwLADN7D5UV1fUdQndfDNwJ7NKck1pFaVZQR9lBnSpJnOWHhrqpNjuJ3e6jk9gu\nNj+JvfH2WklsyJaBgeDeOtUc9gq0lwdmg8MD3emB7juB7qt1xr4k0E4KjnlDoPu3QPdQoBtZZ+yX\ngjvnN0q1Gy/Na00Q3YkfteCAuN1BX7TggLhaQWSciKofNGKcgHxTQq5xIldXZOxGDBGRGQJiQ0Ru\na42ockhklIm+PxBXLXkss4VM+7DOf+u3L++jShK9Y5K4AzgAeBTYDJgG3Gxm76eSnJzKiqmWBdXX\nmkppEpQQQoiCdHeJ75mZlUctyxat9pDuNXZqeNDM7gKeAb4APNKjefYQJSghhOivvLut8qhl4Ty4\nNt8C7+6LzOwxYCRwE2BUDBS1q6jhwL0NzjZBe1BCCNGq9N4e1ErMbAiV5PSiuz8FzAfG1by+AbAz\ncFtD5xKgFZQQQrQqveDiM7MzgKuoXNZ7F/BtKk09flGVnAkcZ2aPA08DJwHPA7MKzqRbSpOgTveL\n2NR/v/L52XZuqLvcJyaxfWxeEnvM353Etl0nbZziLwQGgg/VqahwfaDdJzAb/DTQfT3QHRfoflBn\n7IMC7RXBMccHutsC3ahA93idsbdItYMXptqoBccWmRvPUQsOiNtw9EULDojNE31hnIDG2nU0YrCo\np222ISIyQ0C+IaKR1hpRJRKIjTrR9zKqmLLJss6VJAb0VSWJ3rGZbw78HBgGvALcCnzY3V8DcPfT\nzWw94DxgKHALMN7dlxacSbeUJkEJIYQoSC+4+Ny9bfUKcPdpVNx9vYoSlBBCtCr9vFisTBJCCCFK\niVZQQgjRqvTzFZQSlBBCtCpKUH3D1+1LnUodTffDQ91RljoZb/K0BNTu9kwSe83XT2LD3hU43B6o\nU/JnXKD9deCG+3Kg+16gOznQHVln7AsC7b7BMWcHut0C3f2BLugRBWDPBaVdNul5j6ioVEzUIwri\nPlFR357ImRU5uKLSN5GzD2J3X184+6CxflKN6Oppcx2IuY696OcD8c8y17EX9QSLSmBF3x+Iez89\nGWijHmc+vPNuiS/ro1JHSlBCCCFKSe/U4isNhUwSZWpkJYQQ73j6oJLEmqQnLr5SNLISQgjRv+nJ\nJb5SNLISQoh3PNqDSnivmb0AvA3cDhzj7s/Va2RlZh2NrFaboE71n7Ox37Ly+bl2Tqi72L+QxPaz\n25PYg/7eJPZ+W5LE2l9LfwQDPlCn5M+tgdngs8GG6cWB7r8D3YmB7vt1xj4s0F6a2SPq5p73iIK4\nT9SAV3reI2p+Zo8oiM0T0Wb2LZnGiWgjPTJOQH5ZpGYbJyA2G0SmhFzzQpEyS5E2mmeuISIqXxT9\nfCDfEBH1+opKW0Xfi6jHGOT3flqyQaob8rfOpY6stUsdlYaiCao0jayEEOIdTz83SRRKUL3ZyOq2\no65g8Ibrrnw+0W5g8uTJtLV1WxZKCCHWGJcvc34zYUKn2KJFq28K2DS0gqpPMxtZ/dv0SWw8eouV\nz8+1qY1MTQgh+oR91jIOvPLKTrF58+Yxpi8u8fVzGqrFtyYbWQkhxDuedioroiKP9vBIpaTQCqo3\nG1l9077YqZLEyf61UHecpV6La/0jSezj9pck9pJvlMQ2GxYYCJ6sU1Fh10A7JzAb7Bfozgt0x+f1\niAKwHwfa/ZvcI2pMnbGDPlG+VV6PqGhDeUSw8fxcnbv7I/NE1Lcn2viONsijygKRcQLyq040YpyI\nDASQX30h17yQq6unjcbONUTk9nOCxgwRN2b2Dou+P5Df+yky/vjWXSpJ/F2VJJpB0Ut8pWlkJYQQ\n73h6YnjoxyaJ0jSyEkKIdzwrqOz8F31Pi6BafEII0aosp3JzTxFaKEGpYaEQQohSUpoV1Lf8Nwzz\nuSufz7AzQt0FPiWJHWR/SGJz/f1JbIwtTGJvvL1WEhuydZ2KCvcGZoO9MltwfKXnLTggbsNhMxpo\nwbFHoJtbZ+xRgfbp4JhbpLr1F6e6Reului3q3N0ftTuINrObbZyA/KoTucaJyBgQGQigMZNFrnkh\n0tXTRmNHc8w1RERmCOgbQ0T0/YHYqBN9L32zoLLK/DVYSaLoCqq/uviEEEKUiJ7YxvvIYNgMlKCE\nEKJVaaH9pJ6gPSghhBClRAlKCCFEKSnNJb6T7DOdKkkc6yeEulPskiR2hY9PYpPswST2mL87iW27\nzrIk5gvqVFT4ULBh2uwWHKfWGTtow5HdguPzge6GQLdbnbHvD7TvC475XN6G8oZv5hknALYONqn7\nwjgBsXni2kzjRLTZHxkDIoMFNGayaMS8UEQbzTE6n+i861XvaMQQcU+g2yHz+wPxdy1qIRNVTPEP\ndKkk8VYLbfSUGK2ghBBClBIlKCGEEKWkNJf4hBBCFGU5lXrdRd/TGihBCSFEy9K/W+qWJkH9j1/D\nUH905fNf27dD3Vl+aBKbarOT2E2+SxLb3Z5JYmELjuF1KioEbTgaasHx00D3zTpjTwu0UQuOQwLd\nLwPdpEB3c52x/y3QPhQcc7tA91LPjRMQmycaMU48lGmcALgj0H48cxM/2uzPrUwB+SaLSNeIeaHR\nsaPziYwl9ap3RIaV3AoRuYaI6PsDcWuYqBKKjwwqSTyxhipJ9MIKysyOAT4DbAe8RaWf39Hu/liN\n5mfAl7q89Rp3/2TByawW7UEJIYSoZSzwAyrNZvcE1gKuNbN1u+hmU+mYPqL66LbbRVFKs4ISQghR\nlKI4h4EAAArmSURBVOZ3LOy6CjKzA4CXgTFUegB28Hd3f6Xg4IXQCkoIIVqWjkt8RR6F96CGUqng\n17Xa9u5mtsDMHjGzH5lZul/SIFpBCSFEy9K7Lj4zM+BM4FZ3/3PNS7OBXwFPAdsApwG/M7Nd3L1p\ndykrQQkhRMvS3SW+K6uPWv5WZIAfAf8C/Htt0N0vq3n6kJk9ADwB7A7cWGSA1VGaBPV/7ROdSh39\nl58e6s62c5PYxf6FJLaf3Z7EGukRBXGfKH8gs0fUrED35UB3Tp1yQ9MC7XHBMX8S6A4KdFcEur3r\njH1boI2cfY8019kH+WWRImdW1N/nfZnOPoAPZ5bTiVxmuX2nIgcgxC7AyA2Xq8t11zU6dnQ+kfMx\nckhC7KjM7emU69iL3HpQx7G3VWYvtF27lDp6oyyljiZUH7U8COzd7TvN7IfAJ4Gx7v7S6rTu/pSZ\nvQqMpD8mKCGEEEXpnUt81eQ0EfiIuz+bod8cGAasNpEVRQlKCCFalua7+MzsR1Qs4xOAJWY2vPrS\nInd/28zWB06gsgc1n8qq6bvAY8CcgpNZLUpQQgjRsvTKCupQKq69m7rEDwRmUMlw/wrsT8Xh9yKV\nxHS8uxedzGpRghJCiJal+aWO3H21tx+5+9vAJwoO2iNKk6AO85vZwF9Y+fw6+3qoO9G/kcSOt8uS\nWLN7RAG0vxaUOPlAsGF6d7CxOjHQXR7oDq9TbuisQHtycMxvBLoLMo0TV9UZOzBPNGSciHpJBcYJ\nAN8iryxStPG9RbBBPj/TOAHxpntUTie3fFKuwQLyyyxFZoxGdEW00RxzyxJFBhSAxzINEZEBJtcQ\nEZkhoIAhYufg98Bd/afUUZnQjbpCCCFKSWlWUEIIIYrSfJNEmVCCEkKIlqV/X+JTghJCiJZFK6g+\n4ce2W6dKEvv7+aFuhn0nieX2iLred01i44IeUU/7iHDsrYYFG6YvBBurOwa6WwPdPoFuZp1qDlMD\n7feCY36nucYJiM0T2caJ3TJ7SQXGCQB7Lu/u/mjju32TVDci2EiPKlNAvOmea7JoxGABsYkgMhvk\nVl7I1dXTRvOM5phrcoh+PgDbBtpXB+cZYJZulNnPKfj+QB1DxJjg+zs30E3oUkni9b6qJKEVlBBC\niFLSvxOUXHxCCCFKiVZQQgjRsmgPSgghRCnp35f4SpOgJvuDrOurfnD328GhLmrDEbXguMCnJLGD\n7NYkdovvmMTG2vxw7Jc8bRi52buCDdNng43VXTONE2117nIPzBP2371vnID8qhM+KdDdHOj2yDNO\nQJ1N6mgzO2jrMeCVQJdZmQLiTfdck0VksIg2++tVsYgqJeRWVMg1JUS6eseM5hkZRnJNDtHPB+LK\nDxsvzWvPMnhhoBuZ9/2BuEJEaIgIDEIDrl6TlSSaW+qoTJQmQQkhhCiKVlBCCCFKSf/eg5KLTwgh\nRCkpXYJ6fea1a3oKTWXmrLK0fm6cmU/2n3MBmPlm/zqfWd5/zufyZf3nXHqXjkt8RR66xFeYX9j7\nGW2jmXjpKcz64nF8zK8KdVEbjm/4iUnsO3ZJErvYv5DE9rO7k9jtPjqJAexiC5PYy75hEtt0y1Vf\ngEt/P5EvfnVWQ8YJiM0TYbuOyDgRteqIjBPT6oxdNU9cOnEiX7xgVkV7WHDMK4JjTgl0NwS68XXG\njjapo+oUUVuPyGBRU5ni0okT+eKsWaHBAupsugdVCCKTRbSJH232R0YMiCsldNdS5LqJEzli1qxQ\nl9uKot7YuYaRqHpHrskBVlV++M3EiRwwq/pdi4wOQXsWHxXoHs/7/gDYnZnGn8ggdESXShKv9FWC\n7d+X+EqToIQQQhRFJgkhhBClpH+voEq3ByWEEEJAOVZQ6wA88sgjALz++uvMmzePxf5EKJ5n85LY\nfH8xS/e0/zVL96i/GY69dqBd6OlfIxvV6DrOx+en16Tt1fR4/mh87drWC7SBacHmBbrnMnUv1Rm7\nqu04F4ivsYfHXJipW7z6sTtp38g8ZmCCqNWt/GzeLjD20syxg03+SLdseTz2WoH2rRWpdt3gfLrT\nre549bTRPKM5tge6AZk/H6jzXft75s/8rUxd8P2pqw2qkkc6uvx7eGTVr5p1wsGaxosUX0G93BsT\n6RXM17Dzx8y+CKSOBiGEaH2muPvPm31QM9sSeBhYr4eHeBPY3t2fbd6smk8ZEtQwYC/gaeDtNToZ\nIYRoDusAWwFz3P213higmqQ27uHbXy17coISJCghhBAiQiYJIYQQpUQJSgghRClRghJCCFFKlKCE\nEEKUEiUoIYQQpaQ0CcrMDjezp8zsLTO7w8zSVrclxMzGmtmVZvaCmbWb2YRAc6KZvWhmb5rZdWY2\nck3MtTvM7Bgzu8vMFpvZAjP7jZltG+ha5XwONbP7zWxR9XGbmX2ii6YlzqUrZvaN6vdtepd4S5yP\nmZ1QnX/t489dNC1xLqL3KEWCMrN9ge8BJwAfAu4H5phZTz3+fcn6wH3AfwKJZ9/MjgaOAA4BdgKW\nUDm3wX05yUzGAj8Adgb2BNYCrjWzdTsELXY+zwFHA6OBMcANwCwz2x5a7lxWUv3j7RAq/05q4612\nPg8Cw4ER1ceuHS+04LmI3sDd1/gDuAM4q+a5Ac8DX1/Tcyt4Hu3AhC6xF4Eja55vALwFfGFNzzfj\nfDauntOu/eF8qvN9DTiwVc8FGAI8CuwB3AhMb8XPhsofo/NW83rLnIsevfdY4ysoM1uLyl+313fE\nvPKN/D2wy5qaVzMws/dQ+cuw9twWA3fSGuc2lMqqcCG09vmY2QAzm0ylNMxtLXwu5wBXufsNtcEW\nPZ/3Vi+NP2FmF5vZFtCy5yJ6gTIUi90YGAgs6BJfAPxz30+nqYyg8gs+OrcRfT+dfMzMgDOBW929\nY2+g5c7HzN4P3E6l9MzfgM+4+6Nmtgutdy6TgQ8COwQvt9pncwdwAJXV4GbANODm6ufVaucieoky\nJChRTn4E/Avw72t6Ig3yCDAK2BD4PDDDzHZbs1MqjpltTuUPhj3dvWiHutLh7nNqnj5oZncBzwBf\noPKZCbHmL/EBr1LpoDW8S3w4ML/vp9NU5lPZT2upczOzHwKfBHZ395dqXmq583H35e7+pLvf6+7H\nUjEWTKX1zmUMsAkwz8yWmdky4CPAVDNbSmV10Urn0wl3XwQ8Boyk9T4b0Uus8QRV/WtwLjCuI1a9\nvDQOuG1NzasZuPtTVP5B1Z7bBlRccqU8t2pymgh81LtUO27F8wkYAKzdgufye+ADVC7xjao+7gEu\nBka5+5O01vl0wsyGUElOL7bgZyN6ibJc4psOXGhmc4G7gCOpbGZfuCYnlYOZrU/lH5ZVQ1ub2Shg\nobs/R+WyzHFm9jiVliInUXEozloD010tZvYjoA2YACwxs46/YBe5e0crlFY6n1OB2cCzwD8AU6is\nOj5elbTMubj7EqDrfUJLgNfc/eFqqGXOx8zOAK6iclnvXcC3gWXAL6qSljkX0YusaRthx4PKfURP\nU7GS3g7ssKbnlDnvj1CxYq/o8rigRjONim32TWAOMHJNz7vOuUTnsQLYv4uuVc7np8CT1e/UfOBa\nYI9WPJc653cDNTbzVjofYCaVhPMWlT8gfg68pxXPRY/ee6gflBBCiFKyxveghBBCiAglKCGEEKVE\nCUoIIUQpUYISQghRSpSghBBClBIlKCGEEKVECUoIIUQpUYISQghRSpSghBBClBIlKCGEEKVECUoI\nIUQp+f8BzAf3Pp9zgQkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa868d5ac>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log(np.array(inv_hilbert).astype(float)), \n",
    "           interpolation='none')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Was ist das Problem?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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izTXqKPU9Ot8fdDs7O8vMzEy2//DmGH6Cu0EnyMAM8CGagI4EvLnXfhVwcUrp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa83e64cc>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12, 5))\n",
    "fig.add_subplot(121)\n",
    "plt.imshow(np.log(abs(np.array(inv_hilbert).astype(float))), \n",
    "           interpolation='none')\n",
    "plt.colorbar()\n",
    "fig.add_subplot(122)\n",
    "plt.imshow(np.sign(np.array(inv_hilbert).astype(float)), \n",
    "           interpolation='none', cmap=plt.cm.hot)\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Als Ersatz für 3D-Plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = Symbol('y')\n",
    "f = cos(sqrt(x**2+y**2))\n",
    "fn = lambdify((x,y), f, 'numpy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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U3bsB/BqAbwDww5cyKIHoZ3KUAuTrbMfJ1kPJosdNndstldsEt5IleTxCrkKt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G2WKl2ubM36f8iZmGVeLmqHMFpVRjw3zuLebJRYiuEkS3XlAlVWpebifFDclDHPoIwJ0rND+vxV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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa81ad30c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-2*np.pi, 2*np.pi, 150)\n",
    "y = x\n",
    "X, Y = np.meshgrid(x, y)\n",
    "W = fn(X, Y)\n",
    "plt.imshow(W, origin='lower', cmap=plt.cm.coolwarm)\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAo4AAAAUBAMAAADxQqHfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ntTvNFXvR6jSUmP8xCzn4B+iZq5yj1NqnAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( -6.28318530718, \\quad 6.28318530718, \\quad -6.28318530718, \\quad 6.28318530718\\right )$$"
      ],
      "text/plain": [
       "(-6.28318530718, 6.28318530718, -6.28318530718, 6.28318530718)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "extent = (x[0], x[-1], y[0], y[-1])\n",
    "extent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "W[W<0] = -W[W<0]  # abs(W) wäre einfacher"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j/KsA/uqDTlpBnt+xINr3hSmt4YscLBjZqq/bAgJACkq6tAzJAtOzIJHgpWVJVuigwHRp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\ncZ9VFt1LgSQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa86846ec>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(W, origin='lower', cmap=plt.cm.hot, extent=extent)\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lineare Gleichungssysteme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAABLCAMAAADDCbAzAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nA4rTJ9/R0sTwAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  2  3⎤\n",
       "⎢       ⎥\n",
       "⎢4  5  6⎥\n",
       "⎢       ⎥\n",
       "⎣7  8  9⎦"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix(3, 3, range(1,10))\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACUAAABLCAMAAADAvr4bAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nHaBiJjF6AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}6\\\\15\\\\24\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡6 ⎤\n",
       "⎢  ⎥\n",
       "⎢15⎥\n",
       "⎢  ⎥\n",
       "⎣24⎦"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = Matrix([6, 15, 24])\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir wollen $Ax=b$ lösen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACUAAABLCAMAAADAvr4bAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nCT8lSBs6vn2GPwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x_{1}\\\\x_{2}\\\\x_{3}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡x₁⎤\n",
       "⎢  ⎥\n",
       "⎢x₂⎥\n",
       "⎢  ⎥\n",
       "⎣x₃⎦"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = Matrix([Symbol('x_'+str(j)) for j in [1,2,3]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAABLCAMAAACr1vBOAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n+Zcl+o8c9Rl2wSt+BGSt63+FIWnvII/mCwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x_{1} + 2 x_{2} + 3 x_{3}\\\\4 x_{1} + 5 x_{2} + 6 x_{3}\\\\7 x_{1} + 8 x_{2} + 9 x_{3}\\end{matrix}\\right] = \\left[\\begin{matrix}6\\\\15\\\\24\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡ x₁ + 2⋅x₂ + 3⋅x₃ ⎤ = ⎡6 ⎤\n",
       "⎢                  ⎥   ⎢  ⎥\n",
       "⎢4⋅x₁ + 5⋅x₂ + 6⋅x₃⎥   ⎢15⎥\n",
       "⎢                  ⎥   ⎢  ⎥\n",
       "⎣7⋅x₁ + 8⋅x₂ + 9⋅x₃⎦   ⎣24⎦"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glg = Eq(A*x, b)\n",
    "glg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPAAAAAVBAMAAACK8n6QAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n",
      "text/latex": [
       "$$\\left [ \\left \\{ x_{1} : x_{3}, \\quad x_{2} : - 2 x_{3} + 3\\right \\}\\right ]$$"
      ],
      "text/plain": [
       "[{x₁: x₃, x₂: -2⋅x₃ + 3}]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Lsg = solve(glg)\n",
    "Lsg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACoAAAAPBAMAAABgjEDtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA782r3SJ2ZjIQmUS7\nVIlAnjihAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVQYGWNg/GQs72z0hQEV8Acw5BcwNKIK\nMsxiAIkyo4mGg0XZJqAKR4BFOUCi0Q2c3QFwWaAJ3Iq5j0LXH+A9n8DAuvwxWAooysC4dn4B0wEG\n/gSGLRO4JUEaQKJMDgwMPGBROQYGMaAgRNQAKsrxq7zcHC66ACrK/hckBARgExbA1H4DiyFEmQ8w\nxCcwODEwTIOpZQGqZRdguHiSob+AYSUDA/caeZkV3Of/XGBgeJc2RWQCp1XeBKghaBQAM0c287zN\nvm0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\mathrm{True}$$"
      ],
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glg.subs(Lsg[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "konkrete Lösung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABoAAABLCAMAAABZRmeuAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAo1xBWAAAAE3RSTlMA\nMquZdlQQQOkwRIlmzd0i77ts7uXj/QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAASJJREFUOBHtlVmC\nwyAIQEldplXrMtz/rhWIiaTOXKDlIzE8QYKgsCHLDQ7JogHY0Ngu7iCQ6PuGhLZTe46SQt7EFMc8\njZ7dqc9FLBVKlZTxuUCNg3TomSkrZBRQYp2RR0PTA9o3q4KRdJu8YLYqYrVC/zgECcMtwoDWaK20\nCl5+2ax+GTIlqu5JnCPs6tj3Yp1eWuoQbXWoafDxqMQY2yhwlY1CZeMwSb4Usry/mBco1NA3Bpdb\nSdPXDon4zMXYR2otgBKzkYp/Q31ypAVJLlakqvXslJ/7g1TdHTdd20v09z71MnJxDqQcVq7ejNKx\nCiVKkdvb6xJGMMa0PcAL4mDGQzkcSnl/PPqeolOJfk9RvmH/vLI9XdDWjpbrLcRXtrXwAlM/GfOZ\nJfpqAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}0\\\\3\\\\0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡0⎤\n",
       "⎢ ⎥\n",
       "⎢3⎥\n",
       "⎢ ⎥\n",
       "⎣0⎦"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.subs(Lsg[0]).subs(x[2], 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "andere konkrete Lösung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABoAAABLCAMAAABZRmeuAAAANlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABHL6OuAAAAEXRSTlMAMquZdlQQ\nQOkwRO/NZt0ibN6FPU8AAAAJcEhZcwAADsQAAA7EAZUrDhsAAACTSURBVDgR7ZVLDoAgDERLqfjF\n2PtfVtFYqFGj7DR0BR26eUwzYHgtBKlx6wAYtrRUJQr4cEcOkondePLPpap3+5yacmiRz6XlPRVJ\nyFvseUC/UVQMd7BF0iTC7QWoP1m0blphkSzR1OhdTqQjqBypWFTjlS945cObqT9ZNM2UHLPlpcMn\nLXoZ2S4ENFEXLbNGNhHMBz8UhIpZS1MAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1\\\\1\\\\1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1⎤\n",
       "⎢ ⎥\n",
       "⎢1⎥\n",
       "⎢ ⎥\n",
       "⎣1⎦"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.subs(Lsg[0]).subs(x[2], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMMAAAAVBAMAAAAJNkerAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left \\{ x_{1} : x_{3}, \\quad x_{2} : - 2 x_{3}\\right \\}$$"
      ],
      "text/plain": [
       "{x₁: x₃, x₂: -2⋅x₃}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(A*x, x)  # Kern von A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAUBAMAAABCNWFYAAAAG1BMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAB4Gco9AAAACHRSTlMAdt3NMolEZgN4ymIAAAAJcEhZcwAADsQAAA7EAZUrDhsA\nAAAXSURBVAgdYxAyKVZjCGMAIpoQQipCagCy4Q1mVUJFwQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ \\right ]$$"
      ],
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(A*x, Matrix([0,0,1]))  # unlösbar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Veränderliche und unveränderliche Matrizen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "B = A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAABLCAMAAABN0/lPAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}999 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡999  2  3⎤\n",
       "⎢         ⎥\n",
       "⎢ 4   5  6⎥\n",
       "⎢         ⎥\n",
       "⎣ 7   8  9⎦"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[0,0] = 999\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAABLCAMAAABN0/lPAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAo1xBWAAAAE3RSTlMA\nMquZdlQQQOkwRIki72bNu91spdw0jAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAA/NJREFUaAXtWe2y\nnCAMRUB6K4pa3v9dmwRQ0YS1d3ennenyw40Bckz4OmRVF6lo9c6yJhClumgslP6dYCoghI6I1r0V\naDceKjRnvNcj1nLS3usojcYsi/y5o/d+KWGr0NwUlBongOOkI8QuOxxuH4ddU0mjgdc+gl0sFZqe\nUKWhASdh3bVoh7qJel5rlY3oV1xTVYUWZ1R6CC4npQ7n50SGtDT0wwReu2Su9s3FBW3Z2HHSGSa/\nzxGdE9GoFR/JKfs2KE4S4Ei9EqbQwq0+11SRxBgqNcOYcpJgC9VDLPaujUa/GhpbqKrQ1GxhAnkc\nWE66Wiqatb0PeRw8LDUarvjO04hzUupyfRqc5q0yTcm7Exp20dsYcBJj1DbARtorFloHF9/Q1ryF\nhZOuaD2CJavXykifzqIF3Ea6CA9OupoiTUeeWfLh2mSiRbWiTShVJO3slJtxl+Ekan95jCtshEbn\nzeJSHdBaH2H2YanQlDfGpOnDSanH6Tmnc0tCUwOYXMouWqOdLL389YP2qpB+IvmJ5OMI/K+zJO3u\nj+IzW6c6U/gp09p76zO7bUVypdOC6V+pJtyWZVriZtiSDdGr8xlQmbHpbKp0zMvstXS4YesFj78l\nf7fs2xjmW75tJz3zJcjGjsesjObVK9CWirKLaGG8ixaCNeIdJ86dt/mElsfNwdl+z7cFyNso3XHg\nBoBUYcpTVvINJ9k9NBquRWAKLnEuI/NJ7N5jaP4AzVSTgT4gPdJdKmTf0bcfXz8P9Sg6Wj+30PR2\nUznZSK8rVYd8Xfz1xd27e40lTjozM9ZQUqbbkNn49alpunYefZNu+bdWd2LlyYUTEr529BkmrwNp\nlmDLdHlEqVHoYk3Umm+kYVDcozkJF+IlRp1v57yhpB2N19sFjWkIPFiX5djyjen6pOqD9mQAt+6f\nSG6heFL4RPLJAG7d/4lIdquGNCyU7bNEwVnrN+JxbbUncaFO8C2kTEFs0zeyTUeOlrjynsTFxgKa\nSSzwBlhPx8SYyTDhHx97EreBliJY6Pux+1n2RHGdwIIOSdwGGtkcHvMEJMNI8bxwEO5JXLIoRJLq\nbhFzSPnFIIEBk6xIUgNNNkHfsj18jJAfE8qexMUGMpqjtK9g5KDu9bDGklw96LO4J3FBIaNZaZrV\nFgPOWxszGa7r6G1P4rbQ7t0VFaY0kchJC44QSxJX9M3dWdn4xwKZU212VpK4Ihr8TZbsPHgm39Ry\nvBQeuuxJXFSKaP1NtIHmY5CW5p7EbaKNhd8ePpQVO9i/G7vynsRt+cZaflYpRvJZw2z/Dxoblm8o\n/0YkiRfcOKi/4U7psv27DjwGS/lDotS/9pf+XbdW/QYIVy6/2x4VZQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}999 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡999  2  3⎤\n",
       "⎢         ⎥\n",
       "⎢ 4   5  6⎥\n",
       "⎢         ⎥\n",
       "⎣ 7   8  9⎦"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAABLCAMAAABN0/lPAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}777 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡777  2  3⎤\n",
       "⎢         ⎥\n",
       "⎢ 4   5  6⎥\n",
       "⎢         ⎥\n",
       "⎣ 7   8  9⎦"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = A.copy()\n",
    "B[0,0] = 777\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAABLCAMAAABN0/lPAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}999 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡999  2  3⎤\n",
       "⎢         ⎥\n",
       "⎢ 4   5  6⎥\n",
       "⎢         ⎥\n",
       "⎣ 7   8  9⎦"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAABLCAMAAABN0/lPAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}999 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡999  2  3⎤\n",
       "⎢         ⎥\n",
       "⎢ 4   5  6⎥\n",
       "⎢         ⎥\n",
       "⎣ 7   8  9⎦"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = A[0:3, 0:3]\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIIAAABLCAMAAACLOq+zAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n/wFn9TNZCGceQgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}999 & 2 & 3\\\\4 & 555 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡999   2   3⎤\n",
       "⎢           ⎥\n",
       "⎢ 4   555  6⎥\n",
       "⎢           ⎥\n",
       "⎣ 7    8   9⎦"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C[1,1] = 555\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAABLCAMAAABN0/lPAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}999 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡999  2  3⎤\n",
       "⎢         ⎥\n",
       "⎢ 4   5  6⎥\n",
       "⎢         ⎥\n",
       "⎣ 7   8  9⎦"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.matrices.dense.MutableDenseMatrix"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.matrices.immutable.ImmutableMatrix"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ai = simplify(A)\n",
    "type(Ai)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Ai[0,0] = 3 # TypeError, denn Ai ist ImmutableMatrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASwAAABLCAMAAAD9JUoRAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left ( \\left[\\begin{matrix}999 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right], \\quad \\left[\\begin{matrix}333 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]\\right )$$"
      ],
      "text/plain": [
       "⎛⎡999  2  3⎤, ⎡333  2  3⎤⎞\n",
       "⎜⎢         ⎥  ⎢         ⎥⎟\n",
       "⎜⎢ 4   5  6⎥  ⎢ 4   5  6⎥⎟\n",
       "⎜⎢         ⎥  ⎢         ⎥⎟\n",
       "⎝⎣ 7   8  9⎦  ⎣ 7   8  9⎦⎠"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = Matrix(Ai)\n",
    "B[0,0] = 333\n",
    "A, B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.matrices.dense.MutableDenseMatrix"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(Matrix(B))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameterabhängige Matrizen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH0AAABLCAMAAABqfXinAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n4a99OCf/AKM1K3d8tJ6zAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}a + 1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡a + 1  2  3⎤\n",
       "⎢           ⎥\n",
       "⎢  4    5  6⎥\n",
       "⎢           ⎥\n",
       "⎣  7    8  9⎦"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Symbol('a')\n",
    "A = Matrix(3,3,range(1,10))\n",
    "A[0,0] = 1 + a\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASUAAABLCAMAAAABMGHbAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nitEvcdY5GUO2/wyAta1/AZjtcmIIoVbBAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x_{1} \\left(a + 1\\right) + 2 x_{2} + 3 x_{3}\\\\4 x_{1} + 5 x_{2} + 6 x_{3}\\\\7 x_{1} + 8 x_{2} + 9 x_{3}\\end{matrix}\\right] = \\left[\\begin{matrix}6\\\\15\\\\24\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡x₁⋅(a + 1) + 2⋅x₂ + 3⋅x₃⎤ = ⎡6 ⎤\n",
       "⎢                        ⎥   ⎢  ⎥\n",
       "⎢   4⋅x₁ + 5⋅x₂ + 6⋅x₃   ⎥   ⎢15⎥\n",
       "⎢                        ⎥   ⎢  ⎥\n",
       "⎣   7⋅x₁ + 8⋅x₂ + 9⋅x₃   ⎦   ⎣24⎦"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glg = Eq(A*x, b)\n",
    "glg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOEAAAAVBAMAAABCnpRGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n",
      "text/latex": [
       "$$\\left \\{ x_{1} : 0, \\quad x_{2} : 3, \\quad x_{3} : 0\\right \\}$$"
      ],
      "text/plain": [
       "{x₁: 0, x₂: 3, x₃: 0}"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(glg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARsAAABLCAMAAAB3CtNQAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nT+4AuAr+AcRhbkHwsjxKAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x_{1} \\left(a + 1\\right) + 2 x_{2} + 3 x_{3}\\\\4 x_{1} + 5 x_{2} + 6 x_{3}\\\\7 x_{1} + 8 x_{2} + 9 x_{3}\\end{matrix}\\right] = \\left[\\begin{matrix}0\\\\0\\\\1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡x₁⋅(a + 1) + 2⋅x₂ + 3⋅x₃⎤ = ⎡0⎤\n",
       "⎢                        ⎥   ⎢ ⎥\n",
       "⎢   4⋅x₁ + 5⋅x₂ + 6⋅x₃   ⎥   ⎢0⎥\n",
       "⎢                        ⎥   ⎢ ⎥\n",
       "⎣   7⋅x₁ + 8⋅x₂ + 9⋅x₃   ⎦   ⎣1⎦"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glg = Eq(A*x, Matrix([0,0,1]))\n",
    "glg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVcAAAAyBAMAAAAaUYV2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\naJ7yJVZXR0BPrIQPOl74P4oXV+1Q1ObzAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left \\{ x_{1} : \\frac{1}{a}, \\quad x_{2} : 2 - \\frac{2}{a}, \\quad x_{3} : - \\frac{5}{3} + \\frac{1}{a}\\right \\}$$"
      ],
      "text/plain": [
       "⎧    1          2        5   1⎫\n",
       "⎨x₁: ─, x₂: 2 - ─, x₃: - ─ + ─⎬\n",
       "⎩    a          a        3   a⎭"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(glg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACQAAAAOBAMAAAC1GaP7AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMiKJu1SZZnZE\n76v5rQUQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAkklEQVQYGWNggALWtPQGGBtKRzJw/EIT2t/A\n8BlN6OwBxk9oQgyYGhkYhBMYGCIz9wog1IZZCjDwXGXQR4gwMLDdYZBdwDCdgUHIGARUQHJ3BeYL\nMFgjVIUyMNQ3XGdg/IIQ+i/AUN/4jYHjA0LoOgODfeAPBnaFVrjYKgaO3wzaDIsfJMCFeGZOP8Ag\nt8319QEAZxsj+CfrQIsAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$- 3 a$$"
      ],
      "text/plain": [
       "-3⋅a"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.det()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gauß-Elimination zu Fuß"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArsAAABaCAMAAACPOm6+AAAAQlBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left ( \\left[\\begin{matrix}1 & 0 & 0\\\\\\frac{4}{a + 1} & 1 & 0\\\\\\frac{7}{a + 1} & \\frac{8 - \\frac{14}{a + 1}}{5 - \\frac{8}{a + 1}} & 1\\end{matrix}\\right], \\quad \\left[\\begin{matrix}a + 1 & 2 & 3\\\\0 & 5 - \\frac{8}{a + 1} & 6 - \\frac{12}{a + 1}\\\\0 & 0 & 9 - \\frac{21}{a + 1} - \\frac{\\left(6 - \\frac{12}{a + 1}\\right) \\left(8 - \\frac{14}{a + 1}\\right)}{5 - \\frac{8}{a + 1}}\\end{matrix}\\right], \\quad \\left [ \\right ]\\right )$$"
      ],
      "text/plain": [
       "⎛⎡  1        0      0⎤, ⎡a + 1      2                       3                 \n",
       "⎜⎢                   ⎥  ⎢                                                     \n",
       "⎜⎢  4                ⎥  ⎢             8                       12              \n",
       "⎜⎢─────      1      0⎥  ⎢  0    5 - ─────               6 - ─────             \n",
       "⎜⎢a + 1              ⎥  ⎢           a + 1                   a + 1             \n",
       "⎜⎢                   ⎥  ⎢                                                     \n",
       "⎜⎢             14    ⎥  ⎢                              ⎛      12 ⎞ ⎛      14 ⎞\n",
       "⎜⎢       8 - ─────   ⎥  ⎢                              ⎜6 - ─────⎟⋅⎜8 - ─────⎟\n",
       "⎜⎢  7        a + 1   ⎥  ⎢                        21    ⎝    a + 1⎠ ⎝    a + 1⎠\n",
       "⎜⎢─────  ─────────  1⎥  ⎢  0        0      9 - ───── - ───────────────────────\n",
       "⎜⎢a + 1        8     ⎥  ⎢                      a + 1                8         \n",
       "⎜⎢       5 - ─────   ⎥  ⎢                                     5 - ─────       \n",
       "⎝⎣           a + 1   ⎦  ⎣                                         a + 1       \n",
       "\n",
       "⎤, []⎞\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎥    ⎟\n",
       "⎦    ⎠"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L, U, R = A.LUdecomposition()\n",
    "L, U, R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L*U == A  # aber nur, weil R=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJwAAABLCAMAAACyXR7oAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}a + 1 & 2 & 3 & 0\\\\4 & 5 & 6 & 0\\\\7 & 8 & 9 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡a + 1  2  3  0⎤\n",
       "⎢              ⎥\n",
       "⎢  4    5  6  0⎥\n",
       "⎢              ⎥\n",
       "⎣  7    8  9  1⎦"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix(3,3,range(1,10))\n",
    "A[0,0] = 1+a\n",
    "b = Matrix([0,0,1])\n",
    "A1 = A.row_join(b)\n",
    "A1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKkAAABOBAMAAACpuismAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & \\frac{2}{a + 1} & \\frac{3}{a + 1} & 0\\\\4 & 5 & 6 & 0\\\\7 & 8 & 9 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡     2      3     ⎤\n",
       "⎢1  ─────  ─────  0⎥\n",
       "⎢   a + 1  a + 1   ⎥\n",
       "⎢                  ⎥\n",
       "⎢4    5      6    0⎥\n",
       "⎢                  ⎥\n",
       "⎣7    8      9    1⎦"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def func1(b, j):\n",
    "    return b/A1[0,0]\n",
    "A1.row_op(0, func1)\n",
    "A1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPAAAABSCAMAAABdX6lFAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nhuYAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & \\frac{2}{a + 1} & \\frac{3}{a + 1} & 0\\\\0 & 5 - \\frac{8}{a + 1} & 6 - \\frac{12}{a + 1} & 0\\\\0 & 8 - \\frac{14}{a + 1} & 9 - \\frac{21}{a + 1} & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡       2          3       ⎤\n",
       "⎢1    ─────      ─────    0⎥\n",
       "⎢     a + 1      a + 1     ⎥\n",
       "⎢                          ⎥\n",
       "⎢         8          12    ⎥\n",
       "⎢0  5 - ─────  6 - ─────  0⎥\n",
       "⎢       a + 1      a + 1   ⎥\n",
       "⎢                          ⎥\n",
       "⎢         14         21    ⎥\n",
       "⎢0  8 - ─────  9 - ─────  1⎥\n",
       "⎣       a + 1      a + 1   ⎦"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def func2(b, j):\n",
    "    return b - A[1,0]*A1[0,j]\n",
    "A1.row_op(1, func2)\n",
    "def func3(b, j):\n",
    "    return b - A[2,0]*A1[0,j]\n",
    "A1.row_op(2, func3)\n",
    "A1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das ist aber sehr fehleranfällig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mult_zeile(A, zeilennr, faktor):\n",
    "    B = Matrix(A)\n",
    "    def func(b, j):\n",
    "        return b*faktor\n",
    "    B.row_op(zeilennr, func)\n",
    "    return B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALIAAABLCAMAAADjyS2LAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nOzL3n8Io+IGJxDGI34H4TOF/CiMl+xfJqTOetfV7dQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}a + 1 & 2 & 3\\\\4 & 5 & 6\\\\-21 & -24 & -27\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡a + 1   2    3 ⎤\n",
       "⎢               ⎥\n",
       "⎢  4     5    6 ⎥\n",
       "⎢               ⎥\n",
       "⎣ -21   -24  -27⎦"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = A.copy()\n",
    "mult_zeile(B, 2, -3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def add_zeile(A, quell_nr, ziel_nr, faktor):\n",
    "    B = Matrix(A)  \n",
    "    def func(b, j):\n",
    "        return b + B[quell_nr,j]*faktor\n",
    "    B.row_op(ziel_nr, func)\n",
    "    return B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPAAAABSCAMAAABdX6lFAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nhuYAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & \\frac{2}{a + 1} & \\frac{3}{a + 1} & 0\\\\0 & 5 - \\frac{8}{a + 1} & 6 - \\frac{12}{a + 1} & 0\\\\0 & 8 - \\frac{14}{a + 1} & 9 - \\frac{21}{a + 1} & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡       2          3       ⎤\n",
       "⎢1    ─────      ─────    0⎥\n",
       "⎢     a + 1      a + 1     ⎥\n",
       "⎢                          ⎥\n",
       "⎢         8          12    ⎥\n",
       "⎢0  5 - ─────  6 - ─────  0⎥\n",
       "⎢       a + 1      a + 1   ⎥\n",
       "⎢                          ⎥\n",
       "⎢         14         21    ⎥\n",
       "⎢0  8 - ─────  9 - ─────  1⎥\n",
       "⎣       a + 1      a + 1   ⎦"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPAAAABgCAMAAAAU7Q/jAAAAOVBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & \\frac{2}{a + 1} & \\frac{3}{a + 1} & 0\\\\0 & 1 & \\frac{6 - \\frac{12}{a + 1}}{5 - \\frac{8}{a + 1}} & 0\\\\0 & 8 - \\frac{14}{a + 1} & 9 - \\frac{21}{a + 1} & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡       2          3       ⎤\n",
       "⎢1    ─────      ─────    0⎥\n",
       "⎢     a + 1      a + 1     ⎥\n",
       "⎢                          ⎥\n",
       "⎢                    12    ⎥\n",
       "⎢              6 - ─────   ⎥\n",
       "⎢                  a + 1   ⎥\n",
       "⎢0      1      ─────────  0⎥\n",
       "⎢                    8     ⎥\n",
       "⎢              5 - ─────   ⎥\n",
       "⎢                  a + 1   ⎥\n",
       "⎢                          ⎥\n",
       "⎢         14         21    ⎥\n",
       "⎢0  8 - ─────  9 - ─────  1⎥\n",
       "⎣       a + 1      a + 1   ⎦"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2 = mult_zeile(A1, 1, 1/A1[1,1])\n",
    "A2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMIAAABPCAMAAACOEeoFAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & \\frac{2}{a + 1} & \\frac{3}{a + 1} & 0\\\\0 & 1 & \\frac{6 a - 6}{5 a - 3} & 0\\\\0 & 0 & - \\frac{3 a}{5 a - 3} & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡     2        3       ⎤\n",
       "⎢1  ─────    ─────    0⎥\n",
       "⎢   a + 1    a + 1     ⎥\n",
       "⎢                      ⎥\n",
       "⎢          6⋅(a - 1)   ⎥\n",
       "⎢0    1    ─────────  0⎥\n",
       "⎢           5⋅a - 3    ⎥\n",
       "⎢                      ⎥\n",
       "⎢            -3⋅a      ⎥\n",
       "⎢0    0     ───────   1⎥\n",
       "⎣           5⋅a - 3    ⎦"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A3 = add_zeile(A2, 1, 2, -A2[2,1])\n",
    "A3 = simplify(A3)\n",
    "A3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAABPBAMAAADrfm/qAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n9dcXNjSS/z3Rpf8BwVXqZYg0B+EAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & \\frac{2}{a + 1} & \\frac{3}{a + 1} & 0\\\\0 & 1 & \\frac{6 a - 6}{5 a - 3} & 0\\\\0 & 0 & 1 & - \\frac{5 a - 3}{3 a}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡     2        3                 ⎤\n",
       "⎢1  ─────    ─────         0     ⎥\n",
       "⎢   a + 1    a + 1               ⎥\n",
       "⎢                                ⎥\n",
       "⎢          6⋅(a - 1)             ⎥\n",
       "⎢0    1    ─────────       0     ⎥\n",
       "⎢           5⋅a - 3              ⎥\n",
       "⎢                                ⎥\n",
       "⎢                     -(5⋅a - 3) ⎥\n",
       "⎢0    0        1      ───────────⎥\n",
       "⎣                         3⋅a    ⎦"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A4 = mult_zeile(A3, 2, 1/A3[2,2])\n",
    "A4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPkAAABOCAMAAADVXkBvAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & \\frac{2}{a + 1} & \\frac{3}{a + 1} & 0\\\\0 & 1 & 0 & \\frac{1}{a} \\left(2 a - 2\\right)\\\\0 & 0 & 1 & - \\frac{5 a - 3}{3 a}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡     2      3               ⎤\n",
       "⎢1  ─────  ─────       0     ⎥\n",
       "⎢   a + 1  a + 1             ⎥\n",
       "⎢                            ⎥\n",
       "⎢                  2⋅(a - 1) ⎥\n",
       "⎢0    1      0     ───────── ⎥\n",
       "⎢                      a     ⎥\n",
       "⎢                            ⎥\n",
       "⎢                 -(5⋅a - 3) ⎥\n",
       "⎢0    0      1    ───────────⎥\n",
       "⎣                     3⋅a    ⎦"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A5 = add_zeile(A4, 2, 1, -A4[1,2])\n",
    "A5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQkAAABQBAMAAAD4sJ3cAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & 0 & - \\frac{4 a - 4}{a \\left(a + 1\\right)} + \\frac{5 a - 3}{a \\left(a + 1\\right)}\\\\0 & 1 & 0 & \\frac{1}{a} \\left(2 a - 2\\right)\\\\0 & 0 & 1 & - \\frac{5 a - 3}{3 a}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡           4⋅(a - 1)    5⋅a - 3 ⎤\n",
       "⎢1  0  0  - ───────── + ─────────⎥\n",
       "⎢           a⋅(a + 1)   a⋅(a + 1)⎥\n",
       "⎢                                ⎥\n",
       "⎢                2⋅(a - 1)       ⎥\n",
       "⎢0  1  0         ─────────       ⎥\n",
       "⎢                    a           ⎥\n",
       "⎢                                ⎥\n",
       "⎢               -(5⋅a - 3)       ⎥\n",
       "⎢0  0  1        ───────────      ⎥\n",
       "⎣                   3⋅a          ⎦"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A6 = add_zeile(A5, 1, 0, -A5[0,1])\n",
    "A7 = add_zeile(A6, 2, 0, -A6[0,2])\n",
    "A7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFUAAABNCAMAAADgrtieAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nw8njeOqN9BXCGPEH/O4kc4fbfy4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{1}{a}\\\\2 - \\frac{2}{a}\\\\- \\frac{5}{3} + \\frac{1}{a}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   1   ⎤\n",
       "⎢   ─   ⎥\n",
       "⎢   a   ⎥\n",
       "⎢       ⎥\n",
       "⎢     2 ⎥\n",
       "⎢ 2 - ─ ⎥\n",
       "⎢     a ⎥\n",
       "⎢       ⎥\n",
       "⎢  5   1⎥\n",
       "⎢- ─ + ─⎥\n",
       "⎣  3   a⎦"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = simplify(A7[0:3, 3])\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(A*y) == b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenwerte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAA/BAMAAADecJgJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left \\{ 0 : 1, \\quad \\frac{15}{2} + \\frac{3 \\sqrt{33}}{2} : 1, \\quad - \\frac{3 \\sqrt{33}}{2} + \\frac{15}{2} : 1\\right \\}$$"
      ],
      "text/plain": [
       "⎧      15   3⋅√33       3⋅√33   15   ⎫\n",
       "⎨0: 1, ── + ─────: 1, - ───── + ──: 1⎬\n",
       "⎩      2      2           2     2    ⎭"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix(3, 3, range(1,10))\n",
    "A.eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HkXNWf46m8Gt73m6e2bPWw/t1+HDuXaMlAE1Mf7N65m2C8Eh+nqSb1ZuXcyaf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\nN80NEo5I6/7hgh4gAYlcOlr5/wdwoCcTRmSaFQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ \\left ( 0, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}1\\\\-2\\\\1\\end{matrix}\\right]\\right ]\\right ), \\quad \\left ( \\frac{15}{2} + \\frac{3 \\sqrt{33}}{2}, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}\\frac{- \\frac{24}{- \\frac{3 \\sqrt{33}}{2} - \\frac{13}{2}} + 12}{\\left(- \\frac{3 \\sqrt{33}}{2} - \\frac{13}{2}\\right) \\left(- \\frac{9 \\sqrt{33}}{8} - \\frac{33}{8}\\right)} - \\frac{3}{- \\frac{3 \\sqrt{33}}{2} - \\frac{13}{2}}\\\\- \\frac{- \\frac{12}{- \\frac{3 \\sqrt{33}}{2} - \\frac{13}{2}} + 6}{- \\frac{9 \\sqrt{33}}{8} - \\frac{33}{8}}\\\\1\\end{matrix}\\right]\\right ]\\right ), \\quad \\left ( - \\frac{3 \\sqrt{33}}{2} + \\frac{15}{2}, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}- \\frac{3}{- \\frac{13}{2} + \\frac{3 \\sqrt{33}}{2}} + \\frac{- \\frac{24}{- \\frac{13}{2} + \\frac{3 \\sqrt{33}}{2}} + 12}{\\left(- \\frac{13}{2} + \\frac{3 \\sqrt{33}}{2}\\right) \\left(- \\frac{33}{8} + \\frac{9 \\sqrt{33}}{8}\\right)}\\\\- \\frac{- \\frac{12}{- \\frac{13}{2} + \\frac{3 \\sqrt{33}}{2}} + 6}{- \\frac{33}{8} + \\frac{9 \\sqrt{33}}{8}}\\\\1\\end{matrix}\\right]\\right ]\\right )\\right ]$$"
      ],
      "text/plain": [
       "⎡                ⎛               ⎡⎡      ⎛       12         ⎞                 \n",
       "⎢                ⎜               ⎢⎢    2⋅⎜- ──────────── + 6⎟                 \n",
       "⎢                ⎜               ⎢⎢      ⎜    3⋅√33   13    ⎟                 \n",
       "⎢                ⎜               ⎢⎢      ⎜  - ───── - ──    ⎟                 \n",
       "⎢                ⎜15   3⋅√33     ⎢⎢      ⎝      2     2     ⎠           3     \n",
       "⎢⎛0, 1, ⎡⎡1 ⎤⎤⎞, ⎜── + ─────, 1, ⎢⎢───────────────────────────── - ───────────\n",
       "⎢⎜      ⎢⎢  ⎥⎥⎟  ⎜2      2       ⎢⎢⎛  3⋅√33   13⎞ ⎛  9⋅√33   33⎞     3⋅√33   1\n",
       "⎢⎜      ⎢⎢-2⎥⎥⎟  ⎜               ⎢⎢⎜- ───── - ──⎟⋅⎜- ───── - ──⎟   - ───── - ─\n",
       "⎢⎜      ⎢⎢  ⎥⎥⎟  ⎜               ⎢⎢⎝    2     2 ⎠ ⎝    8     8 ⎠       2     2\n",
       "⎢⎝      ⎣⎣1 ⎦⎦⎠  ⎜               ⎢⎢                                           \n",
       "⎢                ⎜               ⎢⎢            ⎛       12         ⎞           \n",
       "⎢                ⎜               ⎢⎢           -⎜- ──────────── + 6⎟           \n",
       "⎢                ⎜               ⎢⎢            ⎜    3⋅√33   13    ⎟           \n",
       "⎢                ⎜               ⎢⎢            ⎜  - ───── - ──    ⎟           \n",
       "⎢                ⎜               ⎢⎢            ⎝      2     2     ⎠           \n",
       "⎢                ⎜               ⎢⎢           ──────────────────────          \n",
       "⎢                ⎜               ⎢⎢                  9⋅√33   33               \n",
       "⎢                ⎜               ⎢⎢                - ───── - ──               \n",
       "⎢                ⎜               ⎢⎢                    8     8                \n",
       "⎢                ⎜               ⎢⎢                                           \n",
       "⎣                ⎝               ⎣⎣                     1                     \n",
       "\n",
       " ⎤⎤⎞  ⎛                 ⎡⎡                       ⎛       12         ⎞   ⎤⎤⎞⎤\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢                     2⋅⎜- ──────────── + 6⎟   ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢                       ⎜    13   3⋅√33    ⎟   ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢                       ⎜  - ── + ─────    ⎟   ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜  3⋅√33   15     ⎢⎢       3               ⎝    2      2      ⎠   ⎥⎥⎟⎥\n",
       "─⎥⎥⎟, ⎜- ───── + ──, 1, ⎢⎢- ──────────── + ─────────────────────────────⎥⎥⎟⎥\n",
       "3⎥⎥⎟  ⎜    2     2      ⎢⎢    13   3⋅√33   ⎛  13   3⋅√33⎞ ⎛  33   9⋅√33⎞⎥⎥⎟⎥\n",
       "─⎥⎥⎟  ⎜                 ⎢⎢  - ── + ─────   ⎜- ── + ─────⎟⋅⎜- ── + ─────⎟⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢    2      2     ⎝  2      2  ⎠ ⎝  8      8  ⎠⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢                                              ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢             ⎛       12         ⎞             ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢            -⎜- ──────────── + 6⎟             ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢             ⎜    13   3⋅√33    ⎟             ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢             ⎜  - ── + ─────    ⎟             ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢             ⎝    2      2      ⎠             ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢            ──────────────────────            ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢                   33   9⋅√33                 ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢                 - ── + ─────                 ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢                   8      8                   ⎥⎥⎟⎥\n",
       " ⎥⎥⎟  ⎜                 ⎢⎢                                              ⎥⎥⎟⎥\n",
       " ⎦⎦⎠  ⎝                 ⎣⎣                      1                       ⎦⎦⎠⎦"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.eigenvects()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jyUIkKtgjlP8pvUHqzBZK02IsHqZZSEHSz0FnWo7kIRoda/hwVudwy6U+zadM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\nx4imjDP5/x8KNHQiJjycSAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ \\left ( 0, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}1\\\\-2\\\\1\\end{matrix}\\right]\\right ]\\right ), \\quad \\left ( \\frac{15}{2} + \\frac{3 \\sqrt{33}}{2}, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}\\frac{\\frac{256}{13 + 3 \\sqrt{33}} + 64}{\\left(11 + 3 \\sqrt{33}\\right) \\left(13 + 3 \\sqrt{33}\\right)} + \\frac{6}{13 + 3 \\sqrt{33}}\\\\\\frac{\\frac{64}{13 + 3 \\sqrt{33}} + 16}{11 + 3 \\sqrt{33}}\\\\1\\end{matrix}\\right]\\right ]\\right ), \\quad \\left ( - \\frac{3 \\sqrt{33}}{2} + \\frac{15}{2}, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}\\frac{6}{- 3 \\sqrt{33} + 13} + \\frac{\\frac{256}{- 3 \\sqrt{33} + 13} + 64}{\\left(- 3 \\sqrt{33} + 11\\right) \\left(- 3 \\sqrt{33} + 13\\right)}\\\\\\frac{\\frac{64}{- 3 \\sqrt{33} + 13} + 16}{- 3 \\sqrt{33} + 11}\\\\1\\end{matrix}\\right]\\right ]\\right )\\right ]$$"
      ],
      "text/plain": [
       "⎡                ⎛               ⎡⎡      ⎛    4         ⎞                ⎤⎤⎞  \n",
       "⎢                ⎜               ⎢⎢   64⋅⎜────────── + 1⎟                ⎥⎥⎟  \n",
       "⎢                ⎜15   3⋅√33     ⎢⎢      ⎝13 + 3⋅√33    ⎠          6     ⎥⎥⎟  \n",
       "⎢⎛0, 1, ⎡⎡1 ⎤⎤⎞, ⎜── + ─────, 1, ⎢⎢───────────────────────── + ──────────⎥⎥⎟, \n",
       "⎢⎜      ⎢⎢  ⎥⎥⎟  ⎜2      2       ⎢⎢(11 + 3⋅√33)⋅(13 + 3⋅√33)   13 + 3⋅√33⎥⎥⎟  \n",
       "⎢⎜      ⎢⎢-2⎥⎥⎟  ⎜               ⎢⎢                                      ⎥⎥⎟  \n",
       "⎢⎜      ⎢⎢  ⎥⎥⎟  ⎜               ⎢⎢            ⎛    4         ⎞          ⎥⎥⎟  \n",
       "⎢⎝      ⎣⎣1 ⎦⎦⎠  ⎜               ⎢⎢         16⋅⎜────────── + 1⎟          ⎥⎥⎟  \n",
       "⎢                ⎜               ⎢⎢            ⎝13 + 3⋅√33    ⎠          ⎥⎥⎟  \n",
       "⎢                ⎜               ⎢⎢         ───────────────────          ⎥⎥⎟  \n",
       "⎢                ⎜               ⎢⎢              11 + 3⋅√33              ⎥⎥⎟  \n",
       "⎢                ⎜               ⎢⎢                                      ⎥⎥⎟  \n",
       "⎣                ⎝               ⎣⎣                  1                   ⎦⎦⎠  \n",
       "\n",
       "⎛                 ⎡⎡                     ⎛     4         ⎞   ⎤⎤⎞⎤\n",
       "⎜                 ⎢⎢                  64⋅⎜─────────── + 1⎟   ⎥⎥⎟⎥\n",
       "⎜  3⋅√33   15     ⎢⎢     6               ⎝-3⋅√33 + 13    ⎠   ⎥⎥⎟⎥\n",
       "⎜- ───── + ──, 1, ⎢⎢─────────── + ───────────────────────────⎥⎥⎟⎥\n",
       "⎜    2     2      ⎢⎢-3⋅√33 + 13   (-3⋅√33 + 11)⋅(-3⋅√33 + 13)⎥⎥⎟⎥\n",
       "⎜                 ⎢⎢                                         ⎥⎥⎟⎥\n",
       "⎜                 ⎢⎢             ⎛     4         ⎞           ⎥⎥⎟⎥\n",
       "⎜                 ⎢⎢          16⋅⎜─────────── + 1⎟           ⎥⎥⎟⎥\n",
       "⎜                 ⎢⎢             ⎝-3⋅√33 + 13    ⎠           ⎥⎥⎟⎥\n",
       "⎜                 ⎢⎢          ────────────────────           ⎥⎥⎟⎥\n",
       "⎜                 ⎢⎢              -3⋅√33 + 11                ⎥⎥⎟⎥\n",
       "⎜                 ⎢⎢                                         ⎥⎥⎟⎥\n",
       "⎝                 ⎣⎣                    1                    ⎦⎦⎠⎦"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.eigenvects(simplify=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r0Nk+P4K15ddILvzhl6cLBVb2G3MIQBZ3gJROpKbQrWBPIhONJ7FylxkAbQQDcEG2XYHO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\n",
      "text/latex": [
       "$$\\left ( \\left[\\begin{matrix}1 & - \\frac{1}{2} + \\frac{3 \\sqrt{33}}{22} & - \\frac{3 \\sqrt{33}}{22} - \\frac{1}{2}\\\\-2 & \\frac{1}{4} + \\frac{3 \\sqrt{33}}{44} & - \\frac{3 \\sqrt{33}}{44} + \\frac{1}{4}\\\\1 & 1 & 1\\end{matrix}\\right], \\quad \\left[\\begin{matrix}0 & 0 & 0\\\\0 & \\frac{15}{2} + \\frac{3 \\sqrt{33}}{2} & 0\\\\0 & 0 & - \\frac{3 \\sqrt{33}}{2} + \\frac{15}{2}\\end{matrix}\\right]\\right )$$"
      ],
      "text/plain": [
       "⎛⎡      1   3⋅√33    3⋅√33   1⎤                               ⎞\n",
       "⎜⎢1   - ─ + ─────  - ───── - ─⎥, ⎡0      0            0      ⎤⎟\n",
       "⎜⎢      2     22       22    2⎥  ⎢                           ⎥⎟\n",
       "⎜⎢                            ⎥  ⎢   15   3⋅√33              ⎥⎟\n",
       "⎜⎢     1   3⋅√33     3⋅√33   1⎥  ⎢0  ── + ─────       0      ⎥⎟\n",
       "⎜⎢-2   ─ + ─────   - ───── + ─⎥  ⎢   2      2                ⎥⎟\n",
       "⎜⎢     4     44        44    4⎥  ⎢                           ⎥⎟\n",
       "⎜⎢                            ⎥  ⎢                 3⋅√33   15⎥⎟\n",
       "⎜⎣1        1            1     ⎦  ⎢0      0       - ───── + ──⎥⎟\n",
       "⎝                                ⎣                   2     2 ⎦⎠"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T, J = A.diagonalize()\n",
    "T = simplify(T)\n",
    "T, J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAABLCAMAAADDCbAzAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nA4rTJ9/R0sTwAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  2  3⎤\n",
       "⎢       ⎥\n",
       "⎢4  5  6⎥\n",
       "⎢       ⎥\n",
       "⎣7  8  9⎦"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(T * J * T**(-1))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:compana16]",
   "language": "python",
   "name": "conda-env-compana16-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}