Linear mapping/Fixed space/Eigenspace/1/Definition

Fixed space

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

$\varphi \colon V\longrightarrow V$

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