# Endomorphism/Invariant subspace/Definition

Invariant subspace

Let be a field, a vector space over and

a
linear mapping.
A
linear subspace
is called
-* invariant*,
if

holds.

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.