A new and efficient 4x4 matrix formalism for light propagation in general l
inear optical media such as lossy biaxial and optically active materials is
developed. The propagation of light is described in terms of the amplitude
s of the four propagating modes. Closed form analytic expressions are obtai
ned for the 4x4 propagation matrices, based on exact solutions for the eige
nmodes in general linear media.