Editing Hermitian matrix (section)

===Symmetric===

A matrix that has only real entries is [[symmetric matrix|symmetric]] [[if and only if]] it is a Hermitian matrix. A real and symmetric matrix is simply a special case of a Hermitian matrix.

{{math proof|1= <math>H_{ij} = \overline{H}_{ji}</math> by definition. Thus  <math>H_{ij} = H_{ji}</math> (matrix symmetry) if and only if <math>H_{ij} = \overline{H}_{ij}</math> (<math>H_{ij}</math> is real).
}}

So, if a real anti-symmetric matrix is multiplied by a real multiple of the imaginary unit <math>i,</math> then it becomes Hermitian.