A description of polarizing state of light by using group theory: Generator of rotation matrix

The applications of the relationship of correspondence between matrices and group theory is continued. The generators of SU(2) group, SO(3) group in the case of the totally transparent system and generators of unimodular group and Lorentz group in the case of the partially transparent system, which are corresponding to Jonas matrix and Mueller matrix in polarization light system respectively, are represented by using unit matrix, Pauli's spin matrix and sparse matrix. According to theory of matrix calculus, it is obviously that a simplified calculus method for polarization light system can be obtained by using the generators of the groups.