Finite-dimensional K-vector spaces/Isomorphism/Stability concepts/Exercise

Let ${}V$ and ${}W$ be finite-dimensional normed ${}{\mathbb {K} }$-vector spaces, and let

$\psi \colon V\longrightarrow W$

denote an isomorphism. Let

$f\colon V\longrightarrow V$

be an endomorphism, and let

${}g:=\psi \circ f\circ \psi ^{-1}\,$

be the corresponding endomorphism on ${}W$. Show that ${}f$ is stable (asymptotically stable) if and only if ${}g$ satisfies this condition.

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