Hermitian matrix

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: A  Hermitian ⟺ a i j = a j i ¯ {displaystyle A{ ext{ Hermitian}}quad iff quad a_{ij}={overline {a_{ji}}}} A  Hermitian ⟺ A = A H {displaystyle A{ ext{ Hermitian}}quad iff quad A=A^{mathsf {H}}} 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: