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Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by the corresponding Mueller matrices, which contain in an implicit and intricate manner all measurable information on such transformations. The general characterization of Mueller matrices relies on the nonnegativity of the associated coherency matrix, which can be mathematically formulated through the nonnegativity of its eigenvalues. The enormously involved explicit algebraic form of such formulation prevents its interpretation in terms of simple physical conditions. In this work, a general and simple characterization of Mueller matrices is presented based on their statistical structure. The concepts associated with the retardance, enpolarization and depolarization properties as well as the essential coupling between the two later are directly described in the light of the new approach.
Except for very particular and artificial experimental configurations, linear transformations of the state of polarization of an electromagnetic wave result in a reduction of the intensity of the exiting wave with respect to the incoming one. This na
Three ways of constructing a non-Hermitian matrix with possible all real eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and generalized PT symmetry. Parameter counting is provided for each class. All three classes of matrices ha
While any two-dimensional mixed state of polarization of light can be represented by a combination of a pure state and a fully random state, any Mueller matrix can be represented by a convex combination of a pure component and three additional compon
We give an asymptotic evaluation of the complexity of spherical p-spin spin-glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy landscape, including the absolute minimum (the grou
In this paper we {em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be the germs of