If V and W are finite-dimensional and the map f is described by the complex matrix A with respect to the bases \mathcal{B} of V and \mathcal{C} of W, then the map \overline{f} is described by the complex conjugate of A with respect to the bases \overline{\mathcal{B}} of \overline{V} and \overline{\mathcal{C}} of \overline{W}.
