Spectral Theorem for Unitary Matrixes

Theorem

• Let $U\in {\mathbb{F}}^{n\times n}$ be a Unitary Matrix
• Then, there exists a unitary matrix $V\in {\mathbb{F}}^{n\times n}$ such that: $VU{V}^{\ast }=diag(e^{i\theta },\dots ,e^{i\theta n})$ $U$ is unitarily similar to the diagonal matrix