Vector space/Linear mapping/Generalized eigenspace/Definition

For a linear mapping ${\displaystyle {}\varphi }$ on a ${\displaystyle {}K}$-vector space ${\displaystyle {}V}$ and an eigenvalue ${\displaystyle {}\lambda \in K}$,

${\displaystyle {}\operatorname {GeEig} _{\lambda }(\varphi )=\bigcup _{n\in \mathbb {N} }\operatorname {kern} {\left(\varphi -\lambda \operatorname {Id} \right)}^{n}\,}$

is called generalized eigenspace of ${\displaystyle {}\varphi }$ for this eigenvalue.