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In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j: or in matrix form: AHermitian ⟺ A=Ā𝖳. Hermitian matrices can be understood as the complex extension of real symmetric matrices.