Mueller matrices and the degree of polarization

This article shows that only polarizers, retarders, and improper rotation Mueller matrices do not decrease the degree of polarization for any input Stokes vector. On the other hand, a Mueller matrix does not increase the degree of polarization for any input Stokes vector if and only if it has an unpolarized Stokes vector as eigenvector. Furthermore, for any Mueller matrix an unpolarized incident Stokes vector always has the maximum gain in the degree of polarization. It is pointed out that a general Mueller matrix deforms the Poincaré sphere (for input Stokes vectors) into an ellipsoid (for output Stokes vectors). Finally, several inequalities involving the input and output degrees of polarization are derived.