Matrix treatment for partially polarized, partially coherent beams

A matrix method is outlined for dealing with quasi-monochromatic, partially polarized light when spatial coherence is not necessarily complete and propagation occurs along beams. Both spatial coherence and polarization properties are described by a single 2x2 matrix whose elements have the structure of mutual intensity functions. Through a simple example it is shown that this matrix can account for differences that would not be revealed by a scalar treatment or by a locally defined polarization matrix.