A conjugate matrix is a matrix A^_ obtained from a given matrix A by taking the complex conjugate of each element of A, i.e., (a_(i j))^_ = (a^__(i j)). The notation A^* is sometimes also used, which can lead to confusion since this symbol is also used to denote the conjugate transpose. Using a matrix X in a similarity transformation X^(-1) A X of a given matrix A is also known as conjugating A by X. In this case, B = X^(-1) A X and A are known as similar matrices.

complex conjugate | conjugate transpose | similarity transformation | similar matrices