Vector space/K/Finite-dimensional/Adjoint endomorphism/Normal/Exercise

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

$\varphi \colon V\longrightarrow V$

denote an endomorphism. Show that ${}\varphi$ is normal if and only if the adjoint endomorphism ${}{\hat {\varphi }}$ is normal.

Create a solution