Linear mapping/Eigenspace/Definition

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

${\displaystyle \varphi \colon V\longrightarrow V}$

a linear mapping. For ${\displaystyle {}\lambda \in K}$, we denote by

${\displaystyle {}\operatorname {Eig} _{\lambda }{\left(\varphi \right)}:={\left\{v\in V\mid \varphi (v)=\lambda v\right\}}\,}$

the eigenspace of ${\displaystyle {}\varphi }$ for the value ${\displaystyle {}\lambda }$.