A three-by-three polarization ray-tracing matrix method for polarization ray tracing in optical systems is presented for calculating the polarization transformations associated with ray paths through optical systems. The method is a three-dimensional generalization of the Jones calculus. Reflection and refraction algorithms are provided. Diattenuation of the optical system is calculated via singular value decomposition. Two numerical examples, a three fold-mirror system and a hollow corner cube, demonstrate the method.