Hermitian and symmetric matrices

The most important example of unitarily diagonalizable matrices.

Notation: ${}^H$: transpose conjugate

Complex Hermitian: $A=A^H$. Then $A=Q\Lambda Q^H,$ $Q$ complex unitary and $\Lambda$ real.

Real Symmetric: $A=A^T$. Then $A=Q\Lambda Q^T,$ $Q$ real orthogonal and $\Lambda$ real.

Unitarily diagonalizable matrices, Orthogonal matrix and projector