Let $A \in \Bbb R^{n \times n}$ be a diagonalizable matrix and let $f(x)$ be a polynom with $x \in \mathbb{R}$.
To prove: f(A) is diagonalizable.
How can I prove this? Do I need to verify the determinant, rank etc?
Thx!
2026-03-25 09:44:39.1774431879
Diagonalizable Matrix with polynom
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No. All you need to do is to use the fact that, if $P$ is invertible,$$f(PAP^{-1})=Pf(A)P^{-1}.$$