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00925njm 22002777a 4500 dc Espinosa Luna, Rafael author Rodríguez Carrera, David author Hinojosa Ruiz, Sinhué Lizandro author Bernabeu Martínez, Eusebio author 2008 The Mueller–Jones (MJ) or pure Mueller matrix formulation has been reported by using two different matrix transformations in a condensed representation. The possibility to find other transformation matrices is explored. A complete set of unitary operators (R) is found to be closely related with the MJ matrices and with the evolution of pure states on the Poincaré sphere surface. We propose an alternative deduction for the condensed representation of the MJ matrices, obtained by using the Kronecker product operation and use of R unitary matrices as a tool to combine different Mueller matrices and changes of polarized states on the Poincarè sphere surface. Finally, it is shown explicitly that the columns of the transformation matrices are the eigenvectors of the MJ matrix associated to a non-depolarizing optical system and a corollary is established as a criterion to differentiate a Mueller matrix from an MJ matrix. 0030-4026 10.1016/j.ijleo.2007.03.008 https://hdl.handle.net/20.500.14352/51161 http://dx.doi.org/10.1016/j.ijleo.2007.03.008 http://www.sciencedirect.com Transformation matrices for the Mueller–Jones formalism