Endomorphism/K/Power/Zero convergence/Asymptotically stable/Definition

Asymptotically stable

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

$\varphi \colon V\longrightarrow V$

be an endomorphism. Then ${}\varphi$ is called asymptotically stable if the sequence ${}\varphi ^{n}$ converges in ${}\operatorname {End} _{}{\left(V\right)}$ to the zero mapping.