Some properties of parameters of Lorentz matrices and transitivity equations E. Ovsiyuk, O. Veko, M. Neagu, V. Balan, V. Red’kov Abstract. In the context of applying the Lorentz group theory to polar- ization optics in the frames of Stokes–Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a product of two commuting and conjugate 4 × 4-matrices, L(q,q)= A(q a )A ∗ (q a ); a =0, 1, 2, 3. Mueller matrices of the Lorentzian type M = L are pointed out as a special sub-class in the total set of 4 × 4 matrices of the linear group GL(4, R). Any arbi- trary Lorentz matrix is presented as a linear combination of 16 elements of the Dirac basis. On this ground, a method to construct parameters q a by an explicitly given Lorentz matrix L is elaborated. It is shown that the factorized form of L = M matrices provides us with a number of simple transitivity equations relating couples of initial and final 4-vectors, which are defined in terms of parameters q a of the Lorentz group. Some of these transitivity relations can be interpreted within polarization op- tics and can be applied to the group-theoretic analysis of the problem of measuring Mueller matrices in optical experiments. M.S.C. 2010: 22E43, 78A10, 81V80, 53B30, 53C50, 83A05, 22E70. Key words: Stokes-Mueller formalism; Lorentz group; transitivity relations; Dirac basis; polarization optics. 1 On establishing the parameters of Lorentz matrices from their explicit form In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes–Mueller formalism, some properties of the Lorentz group are investigated (see [3]-[9]; the notation according to [2, 9] is used). We start with a factorized representation for Lorentz matrices 1 [ L a b (q, ¯ q ∗ )]= A(q)A ∗ (q) , (1.1) ∗ BSG Proceedings, Vol. 20, 2013, pp. 51-63. c  Balkan Society of Geometers, Geometry Balkan Press 2013. 1 Hereafter, we denote by ”*” the complex conjugation.