diff --git a/pymatsolver/solvers.py b/pymatsolver/solvers.py
index f8d79a4..4d0317c 100644
--- a/pymatsolver/solvers.py
+++ b/pymatsolver/solvers.py
@@ -47,6 +47,8 @@ class Base(ABC):
     __numpy_ufunc__ = True
     __array_ufunc__ = None
 
+    _is_conjugate = False
+
     def __init__(
             self, A, is_symmetric=None, is_positive_definite=False, is_hermitian=None, check_accuracy=False, check_rtol=1e-6, check_atol=0, accuracy_tol=None, **kwargs
     ):
@@ -251,7 +253,13 @@ def _transpose_class(self):
         return self.__class__
 
     def transpose(self):
-        """Return the transposed solve operator."""
+        """Return the transposed solve operator.
+
+        Returns
+        -------
+        pymatsolver.solvers.Base
+        """
+
         if self.is_symmetric:
             return self
         if self._transpose_class is None:
@@ -274,6 +282,23 @@ def T(self):
         """
         return self.transpose()
 
+    def conjugate(self):
+        """Return the complex conjugate version of this solver.
+
+        Returns
+        -------
+        pymatsolver.solvers.Base
+        """
+        if self.is_real:
+            return self
+        else:
+            # make a shallow copy of myself
+            conjugated = copy.copy(self)
+            conjugated._is_conjugate = not self._is_conjugate
+            return conjugated
+
+    conj = conjugate
+
     def _compute_accuracy(self, rhs, x):
         resid_norm = np.linalg.norm(rhs - self.A @ x)
         rhs_norm = np.linalg.norm(rhs)
@@ -308,6 +333,8 @@ def solve(self, rhs):
         if ndim == 1:
             if len(rhs) != n:
                 raise ValueError(f'Expected a vector of length {n}, got {len(rhs)}')
+            if self._is_conjugate:
+                rhs = rhs.conjugate()
             x = self._solve_single(rhs)
         else:
             if ndim == 2 and rhs.shape[-1] == 1:
@@ -331,6 +358,8 @@ def solve(self, rhs):
                 # (which is more common for direct solvers).
                 rhs = rhs.transpose()
                 # should end up with shape (n, -1)
+            if self._is_conjugate:
+                rhs = rhs.conjugate()
             x = self._solve_multiple(rhs)
             if do_broadcast:
                 # undo the reshaping above
@@ -347,6 +376,9 @@ def solve(self, rhs):
         #TODO remove this in v0.4.0.
         if x.size == n:
             x = x.reshape(-1)
+
+        if self._is_conjugate:
+            x = x.conjugate()
         return x
 
     @abstractmethod
diff --git a/tests/test_conjugate.py b/tests/test_conjugate.py
new file mode 100644
index 0000000..4dc2529
--- /dev/null
+++ b/tests/test_conjugate.py
@@ -0,0 +1,46 @@
+import pytest
+import pymatsolver
+import numpy as np
+import scipy.sparse as sp
+import numpy.testing as npt
+
+
+@pytest.mark.parametrize('solver_class', [pymatsolver.Solver, pymatsolver.SolverLU, pymatsolver.Pardiso, pymatsolver.Mumps])
+@pytest.mark.parametrize('dtype', [np.float64, np.complex128])
+@pytest.mark.parametrize('n_rhs', [1, 4])
+def test_conjugate_solve(solver_class, dtype, n_rhs):
+    if solver_class is pymatsolver.Pardiso and not pymatsolver.AvailableSolvers['Pardiso']:
+        pytest.skip("pydiso not installed.")
+    if solver_class is pymatsolver.Mumps and not pymatsolver.AvailableSolvers['Mumps']:
+        pytest.skip("python-mumps not installed.")
+
+    n = 10
+    D = sp.diags(np.linspace(1, 10, n))
+    if dtype == np.float64:
+        L = sp.diags([1, -1], [0, -1], shape=(n, n))
+
+        sol = np.linspace(0.9, 1.1, n)
+        # non-symmetric real matrix
+    else:
+        # non-symmetric
+        L = sp.diags([1, -1j], [0, -1], shape=(n, n))
+        sol = np.linspace(0.9, 1.1, n) - 1j * np.linspace(0.9, 1.1, n)[::-1]
+
+    if n_rhs > 1:
+        sol = np.pad(sol[:, None], [(0, 0), (0, n_rhs - 1)], mode='constant')
+
+    A = D @ L @ D @ L.T
+
+    # double check it solves
+    rhs = A @ sol
+    Ainv = solver_class(A)
+    npt.assert_allclose(Ainv @ rhs, sol)
+
+    # is conjugate solve correct?
+    rhs_conj = A.conjugate() @ sol
+    Ainv_conj = Ainv.conjugate()
+    npt.assert_allclose(Ainv_conj @ rhs_conj, sol)
+
+    # is conjugate -> conjugate solve correct?
+    Ainv2 = Ainv_conj.conjugate()
+    npt.assert_allclose(Ainv2 @ rhs, sol)
\ No newline at end of file