Endomorphism/Stable/Direct sum decomposition/Exercise

Let

${}V=U\oplus W\,$

be a direct sum decomposition of a finite-dimensional ${}{\mathbb {K} }$-vector space ${}V$. Let

$\varphi \colon V\longrightarrow V$

be an endomorphism with the direct sum decomposition

${}\varphi =\psi \oplus \theta \,.$

Show that ${}\varphi$ is stable if and only if ${}\psi$ and ${}\theta$ are stable.

Create a solution