Matrix representations of the vector radiative-transfer theory for randomly distributed nonspherical particles

General matrix representations of the vector radiative-transfer equation for randomly distributed nonspherical particles are given with compact representations of the extinction matrix and the Mueller matrix. The propagation of the coherent Stokes vector and the coherency matrix in such a medium is expressed in matrix form. The extinction matrix is related to the generalized optical theorem for partially polarized waves. The first-order scattering solution of the Stokes vector is given in matrix form, and discussions of the Fourier expansion of the equation of transfer and the limitation of the equation of transfer are given.