Eigenvector/Two mappings/Composition/Exercise

Let

$\varphi ,\psi \colon V\longrightarrow V$

be an endomorphisms on a ${}K$-vector space ${}V$, and let ${}v\in V$ be an eigenvector

of ${}\varphi$ and of ${}\psi$. Show that ${}v$ is also an eigenvector of ${}\varphi \circ \psi$. What is its eigenvalue?

Create a solution