Linear mapping/Eigenvector/Definition

Eigenvector

Let ${}K$ be a field, ${}V$ a ${}K$-vector space and

$\varphi \colon V\longrightarrow V$

a linear mapping. Then an element ${}v\in V$, ${}v\neq 0$, is called an eigenvector of ${}\varphi$ (for the eigenvalue ${}\lambda$), if

${}\varphi (v)=\lambda v\,$

for some ${}\lambda \in K$ holds.