Let $E$ be a finite dimensional vector space over a field $F$ and let $T:E\to E$ be a linear transformation. Let $W\subseteq E$ be a subspace such that $T(W)\subseteq W$. Suppose $T$ is diagonalizable. Is $T$ restricted to $W$ also diagonalizable?
my attempts : yes $ T $ is restricted to W is also diagonlisable because T has distinct eigenvalue
pliz help me and tell me the solution
thanks in advance