Summary: In computer graphics, in the radiosity context, a linear system $Φx = b$ must be solved and there exists a diagonal positive matrix $H$ such that $H Φ$ is symmetric. In this article, we extend this property to complex matrices: we are interested in matrices which lead to Hermitian matrices under premultiplication by a Hermitian positive-definite matrix $H$. We shall prove that these matrices are self-adjoint with respect to a particular innerproduct defined on $\Bbb C^n$. As a result, like Hermitian matrices, they have real eigenvalue and they are diagonalizable. We shall also show how to extend the Courant-Fisher theorem to this class of matrices. Finally, we shall give a new preconditioning matrix which really improves the convergence speed of the conjugate gradient method used for solving the radiosity problem.