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Update 2021-11-25-eigentricks.md
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smashmath committed Sep 16, 2024
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Expand Up @@ -214,7 +214,7 @@ At least *most* of the time, mathematics profesors tend to use matrices with nic

This theorem relies on the fact that the minimal polynomial has a quadratic degree or lower. By the Cayley-Hamilton theorem,

$$(A-\lambda_1I)(A-\lambda_2I)==0$$
$$(A-\lambda_1I)(A-\lambda_2I)=0$$

Now, remember that a vector is in the eigenspace of eigenvalue $$\lambda$$ if it's in $$\ker(A-\lambda I)$$. But,

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