Non-singular Mueller matrices characterizing passive systems

We extended previous results and explained why it is necessary to work with SO(6,1)_e (sub-group of matrices with unit determinant and positive left upper corner element) in order to define a parametric form of an arbitrary non-singular Mueller matrix. The previously proposed solution in Devlaminck and Terrier Definition of a parametric form of nonsingular Mueller matrices. J. Opt. Soc. Am. A 25 (2008) 2636-2643], was just a subset of this one. The issue of transmittance conditions for the matrices generated by this formalism is considered and conditions related to the elements of the polar decomposition are derived and give sufficient conditions to guarantee the transmittance conditions for the product matrix.