Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose. That is, if the element in the j {\displaystyle j} -th row and k {\displaystyle k} -th column of a Hermitian matrix A {\displaystyle A} is some complex number A j k = x + i y {\displaystyle A_{jk}=x+iy} , then the element in the k {\displaystyle k} -th row and j {\displaystyle j} -th column is its complex conjugate A k j = A j k ¯ = x − i y {\displaystyle A_{kj}={\overline {A_{jk}}}=x-iy} , for every pair of indices j {\displaystyle j} and k {\displaystyle k} .