Vector space/K/Finite-dimensional/Normal endomorphism/Definition

Normal endomorphism

Let ${}V$ be a finite-dimensional ${}{\mathbb {K} }$-vector space, endowed with an inner product ${}\left\langle -,-\right\rangle$. An endomorphism

$\varphi \colon V\longrightarrow V$

is called normal if ${}\varphi$ and its adjoint endomorphism ${}{\hat {\varphi }}$ commute.