  The generalized Maxwell equations with arbitrary gauge parameter are
considered in the $11\times 11$-matrix form. The gauge invariance of such a
model is broken due to the presence of a scalar field. The canonical and
symmetrical Belinfante energy-momentum tensors are found. The dilatation
current is obtained and we demonstrate that the theory possesses the dilatation
symmetry. The matrix Schr\"{o}dinger form of equations is derived. The
non-minimal interaction in curved space-time is introduced and equations are
considered in Friedmann - Robertson - Walker background. We obtain some
solutions of equations for the vector field.
