The problem of diagonalization of Hermitian Matrices reduces trivially to the already solved problem of diagonalization of real symmetric matrices.
Consider the following equation:
Separating real and imaginary parts the equation above reduces to:
Observe that if is an eigenvector, then is also an eigenvector with the same . This means that the real matrix that corresponds to a Hermitian C has double the number of eigenvalues and they are all degenerate with multiplicity of 2, i.e., , , , , and so on, and the eigenvectors of C are u + i v and then .