Linear mapping/Fixed space/Eigenspace/1/Definition

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

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

a linear mapping. The fixed space of ${\displaystyle {}\varphi }$ is the eigenspace for the eigenvalue ${\displaystyle {}1}$, that is, the set ${\displaystyle {}{\left\{v\in V\mid \varphi (v)=v\right\}}}$.