Endomorphism/Invariant subspace/Definition

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

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

a linear mapping. A linear subspace ${\displaystyle {}U\subseteq V}$ is called ${\displaystyle {}\varphi }$-invariant, if

${\displaystyle {}\varphi (U)\subseteq U\,}$

holds.