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My question is about linear algebra, especially invariant subspaces and diagonalizability. Here is the question:

Let $A$ be a diagonalizable linear operator on the finite dimensional vector space over a field, and let $W$ be a subspace of $V$ which is invariant under $A$. Let us denote by $A_W$ the restriction of $A$ to $W$. I need to prove that $A_W$ is diagonalizable.

How can I prove that?

thanks for your help...

Tom
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juliet
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1 Answers1

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The minimal polynomial of $A_w$ clearly divides the minimal polynomial of $A$, what does this tell you?

Deven Ware
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