Let $V$ be $n$ dimensional vector space. Let $A$ be a representation matrix of linear map $f$ between $V$ and $V$.
Let $W$ be a subspace of $V$.
Suppose $A$ is not diagonalizable, then is there $W$ such that induced linear map $f'$ between $V/W$ and $V/W$ be diagonizable?
I think Eigen space of $W$ satisfies the condition, but I don't know other subspace satisfies the contain..
Thank you in advance.