The term 'conjugation' occurs in several fields such as grammar and biology, but in mathematics the term can be used in two ways:

Conjugation of a complex number or quaternion or matrix is an operation which negates (multiplies by -1) the imaginary part. The adjoint matrix (sometimes also called the adjugate matrix, Hermitian transpose or conjugate transpose) is formed by taking the conjugate of each element in the matrix and then transposing the matrix.

However, the meaning of conjugation we are discussing here is the following function:

V_{out} = a V_{in} a^{-1}