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The classical adjoint of a matrix LaTeX: A is the transpose of the matrix of cofactors

\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.

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