An exact matrix representation of Maxwell's equations

Matrix representations of Maxwell's equations are very well-known. This is evident from the numerous studies on the close resemblance between the Maxwell equations in spinor form to the Dirac equation. However, all these matrix representations lack an exactness, as they assume the media to be homogeneous or/and time-independent. Moreover the final representation is given in terms of a pair of matrix equations. We present a matrix representation of Maxwell's equations in an inhomogeneous linear medium, in presence of sources. It is shown that such a representation necessarily requires 8 x 8 matrices and an explicit representation for them is presented.