The transfer matrix is proposed to describe the coherent cross-polarization coupling (CPC) induced by a single point-like perturbation (PLP) in optical fibers. This matrix remains independent of the fiber length, making it suitable for characterizing the PLP that have a zero-dimensional impact on fiber length. Consequently, the fiber can be fully characterized by a matrix combining the transfer matrix of CPC and the Jones matrix of the fiber birefringence. The polarization performance of fibers exhibiting both CPC and birefringence is analyzed using the developed combined model.