A conjugate matrix is a matrix obtained from a given matrix by taking the complex conjugate of each element of (Courant and Hilbert 1989, p. 9), i.e.,
The notation is sometimes also used, which can lead to confusion since this symbol is also used to denote the conjugate transpose.
Using a matrix in a similarity transformation of a given matrix is also known as conjugating by . In this case, and are known as similar matrices.