The problem of diagonalization of Hermitian Matrices reduces trivially to the already solved problem of diagonalization of real symmetric matrices.

Consider the following equation:

where

Separating real and imaginary parts the equation above reduces to:

The matrix on the left is clearly symmetric because

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
.