Page "Hermitian matrix" Paragraph 10

Every Hermitian matrix is a normal matrix, and the finite-dimensional spectral theorem applies.

It says that any Hermitian matrix can be diagonalized by a unitary matrix, and that the resulting diagonal matrix has only real entries.

This implies that all eigenvalues of a Hermitian matrix A are real, and that A has n linearly independent eigenvectors.

Moreover, it is possible to find an orthonormal basis of C < sup > n </ sup > consisting of n eigenvectors of A.