Let K {\displaystyle {}K} be a field, V {\displaystyle {}V} a K {\displaystyle {}K} -vector space and
a linear mapping. Then an element λ ∈ K {\displaystyle {}\lambda \in K} is called an eigenvalue for φ {\displaystyle {}\varphi } , if there exists a vector v ∈ V {\displaystyle {}v\in V} , v ≠ 0 {\displaystyle {}v\neq 0} such that
