Hermitian Matrix
If a Matrix is Self-Adjoint, it is said to be a Hermitian matrix. Therefore, aHermitian Matrix is defined as one for which
 | (1) |
denotes the Adjoint Matrix. Hermitian Matrices have RealEigenvalues with Orthogonal Eigenvectors. ForReal Matrices, Hermitian is the same as symmetrical. Any Matrix 
which is not Hermitian can be expressed as the sum of two Hermitian matrices | (2) |
be a Unitary Matrix and 
be a Hermitian matrix. Then the Adjoint Matrix of aSimilarity Transformation is |  |  | |
|  | (3) |
The specific matrix
 | (4) |
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. 209-217, 1985.
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