Factorization of the coherency matrix of polarization optics

We show that the coherency matrix associated with a general depolarizing Mueller matrix can be factorized into the product of a matrix, the coherency matrix factor, and its conjugate transpose. The coherency matrix factor contains all the information in the Mueller matrix, and directly shows useful properties in an illustrative fashion. Propagation through a nondeterministic uniform medium is analyzed. Some examples for simple systems are shown, and an experimental Mueller matrix is considered. The coherency matrix and the coherency matrix factor can be diagonalized, even if the Mueller matrix cannot.