If a Matrix is SelfAdjoint, it is said to be a Hermitian matrix. Therefore, a
Hermitian Matrix is defined as one for which

(1) 
where denotes the Adjoint Matrix. Hermitian Matrices have Real
Eigenvalues with Orthogonal Eigenvectors. For
Real Matrices, Hermitian is the same as symmetrical. Any Matrix
which is not Hermitian can be expressed as the sum of two Hermitian matrices

(2) 
Let
be a Unitary Matrix and
be a Hermitian matrix. Then the Adjoint Matrix of a
Similarity Transformation is
The specific matrix

(4) 
where
are Pauli Spin Matrices, is sometimes called ``the'' Hermitian matrix.
See also Adjoint Matrix, Hermitian Operator, Pauli Spin Matrices
References
Arfken, G. ``Hermitian Matrices, Unitary Matrices.'' §4.5 in Mathematical Methods for Physicists, 3rd ed.
Orlando, FL: Academic Press, pp. 209217, 1985.
© 19969 Eric W. Weisstein
19990525