A square matrix is called Hermitian if it is self-adjoint. Therefore, a Hermitian matrix A = (a_(i j)) is defined as one for which A = A^H, where A^H denotes the conjugate transpose. This is equivalent to the condition a_(i j) = a^__(j i), where z^_ denotes the complex conjugate. As a result of this definition, the diagonal elements a_(i i) of a Hermitian matrix are real numbers (since a_(i i) = a^__(i i)), while other elements may be complex.
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