Endomorphism/Invariant subspace/Definition

Invariant subspace

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

$\varphi \colon V\longrightarrow V$

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

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

holds.