The term adjoint matrix is ambiguous. For a complex matrix, it can mean the conjugate transpose, which combines the transpose with entrywise complex conjugation. In classical matrix terminology, it can instead mean the adjugate matrix, which is the transpose of the matrix of cofactors.

To avoid confusing these different operations, "conjugate transpose" is used in this work for the first, and "adjugate matrix" or "classical adjoint" for the second.

See also

Adjugate Matrix, Complex Conjugate, Conjugate Transpose, Cofactor, Transpose

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Weisstein, Eric W. "Adjoint Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AdjointMatrix.html

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