Obtainment of Mueller-Jones matrix from the outer product of input and output Stokes vectors

Implementation of a theorem that was recently put forward is discussed. The theorem states that there exists a relation between input-output Stokes vectors and complex vectors. Complex vectors are obtained as a result of transformation of Stokes vectors by Z matrices. Z matrices are 4x4 analogues of Jones matrices. Jones matrices and Z matrices can be characterized by one real and three complex parameters. It is shown that, in general, six Stokes vector measurements are needed to find all parameters by the proposed theorem. If one of the complex parameters is zero (optical system has a symmetry) two Stokes vector measurements is enough. Besides the symmetry condition, if the optical system is a pure diattenuator or pure retarder (all nonzero complex parameters are real or pure imaginary), then single Stokes vector measurement is enough to determine the parameters that characterize the optical system.