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Soleillet's theory of light scattering by a random aggregation of dipoles has been extended through Mueller matrix algebra to formulate a matrix for light scattering by an array of oriented dipoles. The proposed matrix reveals certain interesting characteristics of dipolar scattering. Linear relations between the parameters of the Stokes' vectors of incident and scattered beams have been obtained for the case of oriented dipoles. The applicability of the matrix has been indicated in the case of radiations in the horizontal plane from an ungrounded antenna or an array of antennas oriented in the vertical plane, and in polarization studies of light scattering by oriented polymer films and fibers which have completely aligned long‐chain molecules.