Let $V$ be a vector space over a field $F$ and let $A$ be in the endomorphisms of $V$. Then $A$ is called non derogatory if its minimal polynomial $m_A(x)$ is equal to its characteristic polynomial $p_A(x)$.
Assume that $A$ is non derogatory and that $K$ is an $A$-invariant subspace of $V$. Can we conclude that the restriction of $A$ to $K$ is non derogatory? How can we see that?