The structure of matrices that represent a linear transformation of the Stokes parameters of a beam of light into the Stokes parameters of another beam of light is investigated by means of the so-called Stokes criterion. This holds that the degree of polarization of a beam of light can never be changed into a number larger than unity. Several general properties are derived for matrices satisfying the Stokes criterion. These are used to establish conditions for the elements of such matrices.

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... itions that are either necessary, or sufficient or both are presented. General 4X4 matrices are treated and a number of special cases is worked out analytically. Several applications are pointed out.