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Let $A \in \text{M}_{n \times n}(\mathbb{C})$. How do I see that if $\lambda_1, \dots, \lambda_n$ are the eigenvalues of $A$, then for any polynomial $P(\cdot)$, I have that $P(\lambda_1), \dots, P(\lambda_n)$ are the eigenvalues for $P(A)$?

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marked as duplicate by daw, Claude Leibovici, user251257, user1551 linear-algebra Sep 30 '15 at 9:43

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