Linear Algebra Done Right
《Linear Algebra Done Right》 · 第 246 页 · Section 7B「The Spectral Theorem」，Theorem 7.31
Suppose $F=\mathbb C$ and $T\in\mathcal L(V)$. Then the following are equivalent: $T$ is normal; $T$ has a diagonal matrix with respect to some orthonormal basis of $V$; $V$ has an orthonormal basis consisting of eigenvectors of $T$.