An eigenvalue criterion for matrices transforming Stokes parameters

Abstract

Simple eigenvalue tests are given to ascertain that a given real 4×4 matrix transforms the four-vector of Stokes parameters of a beam of light into the four-vector of Stokes parameters of another beam of light, and to determine whether a given 4×4 matrix is a weighted sum of pure Mueller matrices. The latter result is derived for matrices satisfying a certain symmetry condition. To derive these results indefinite inner products are applied.