The transpose of a matrix in which each element has been replaced by its cofactor
The classical adjoint of a matrix A is its transpose matrix of cofactors: Adj(A)_ij = (-1)^(i+j) det(A'^(j,i)), where A'^(j,i) is the transpose of A with j-th column of A and i-th row of A deleted The Hermitian adjoint, A*, is the transpose of the conjugate The latter is generally what is meant by the adjoint in most contexts, and we simply have A*=A' when A is real-valued