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On the symmetry of mathematical description of states and transformation of states in polarization theory

In the theory of interaction of partially polarized light with deterministic polarization devices, the light states and the devices can be characterized on equal footing, in a symmetric manner, by similar parameters. We introduce some basic notions for such a description: the Stokes parameters and the Stokes vector of a device, the Poincaré vector of the device, the polarization strength of the states and of the devices and illustrate the symmetry of this description in the frame of a Poincaré sphere approach. This way one shows that not only all the vectors of the states of polarization, but also all the operators of the deterministic dichroic transformations of states are representable by the compact limited spherical manifold of the points of the Poincaré ball; in other words, the topology of the states and that of these transformation of states are quite similar.