The classical adjoint of a matrix $LaTeX: A$ is the transpose of the matrix of cofactors
$LaTeX: \mbox{adj }A = \left[ A^{i,j} \right]_{i,j}^T,$
where $LaTeX: A^{i,j}$ is the determinant of the submatrix of $LaTeX: A$ formed by removing the i-th row and the j-th column. The Hermitian adjoint (conjugate transpose or Hermitian transpose), $LaTeX: A^*$, is the transpose of the conjugate. We have that $LaTeX: A^* = A^T$ if $LaTeX: A$ is real-valued.