Endomorphism/K/Powers/Bounded/Stable/Definition

Let ${\displaystyle {}V}$ be a finite-dimensional ${\displaystyle {}{\mathbb {K} }}$-vector space, and let

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

be an endomorphism. Then ${\displaystyle {}\varphi }$ is called stable if the sequence ${\displaystyle {}\varphi ^{n}}$ in ${\displaystyle {}\operatorname {End} _{}{\left(V\right)}}$ is bounded.