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...