Unitarily diagonalizable matrices

A matrix $A\in {\mathbb{C}}^{n\times n}$ is unitarily diagonalizable if there is a unitary matrix $Q$ and a diagonal matrix $\Lambda$ so that

$$A=Q\Lambda Q^H$$

Definition: $A$ is normal if and only if $A^{H}A=A{A}^H$.

Property: a matrix is normal if and only if it is unitarily diagonalizable.

Eigenvalues, Orthogonal matrix and projector