Let
be endomorphisms on a K {\displaystyle {}K} -vector space V {\displaystyle {}V} , and let v ∈ V {\displaystyle {}v\in V} be an eigenvector of φ {\displaystyle {}\varphi } and of ψ {\displaystyle {}\psi } . Show that v {\displaystyle {}v} is also an eigenvector of φ ∘ ψ {\displaystyle {}\varphi \circ \psi } . What is its eigenvalue?
