Generalization of the Jones vector for partially polarized radiation carried out by Kakichashvili is given. Partially polarized light is presented as two noncoherent components of mutually orthogonal polarization. The formal operation of amplitude summation of mutually noncoherent components and the symbol of this operation are introduced. The rules of operating with this symbol are determined. The regularity of the Weigert effect is modified for partial polarization of the inducing light. On this basis the modification of the Jones matrix for partially polarized light is made. The rules for the formation of the resulting matrix from the Jones matrices corresponding to the noncoherent components of partially polarized light are determined.
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