Normal endomorphism/C/Self-adjoint and real eigenvalues/Exercise

Let

$\varphi \colon V\longrightarrow V$

be a normal endomorphism on the finite-dimensional ${}\mathbb {C}$-vector space ${}V$. Show that ${}\varphi$ is self-adjoint if and only if all eigenvalues of ${}\varphi$ are real.

Create a solution