Editing Hermitian matrix (section)

===Main diagonal values are real===

The entries on the [[main diagonal]] (top left to bottom right) of any Hermitian matrix are [[real number|real]].

{{math proof|1= By definition of the Hermitian matrix
<math display=block>H_{ij} = \overline{H}_{ji} </math>
so for {{math|1=''i'' = ''j''}} the above follows, as a number can equal its complex conjugate only if the imaginary parts are zero.
}}

Only the [[main diagonal]] entries are necessarily real; Hermitian matrices can have arbitrary complex-valued entries in their [[off-diagonal element]]s, as long as diagonally-opposite entries are complex conjugates.