Solution of the Maxwell field equations in vacuum for arbitrary charge and current distributions using the methods of matrix algebra

A new matrix representation of classical electromagnetic theory is presented. The basis of this representation is a space-time, eight-by-eight differential matrix operator. This matrix operator is initially formulated from the differential form of the Maxwell field equations for vacuum. The resulting matrix formulation of Maxwell´s equations allows simple and direct derivation of the electromagnetic wave and charge continuity equations, the Lorentz conditions and definition of the electromagnetic potentials, the Lorentz and Coulomb gauges, the electromagnetic potential wave equations, and Poynting´s conservation of energy theorem. A four-dimensional Fourier transform of the matrix equations casts them into an eight-dimensional transfer theorem. The transfer function has an inverse, and this allows the equations to be inverted. This expresses the fields directly in terms of the charge and current source distributions