English
Related papers

Related papers: Reduced form of a Mueller matrix

200 papers

Our goal here is to see the space of matrices of a given size from a geometric and topological perspective, with emphasis on the families of various ranks and how they fit together. We pay special attention to the nearest orthogonal…

Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have…

Machine Learning · Statistics 2010-12-07 Daniel Hsu , Sham M. Kakade , Tong Zhang

We experimentally investigate the depolarizing power and the polarization entropy of a broad class of scattering optical media. By means of polarization tomography, these quantities are derived from an effective Mueller matrix, which is…

Optics · Physics 2007-05-23 Graciana Puentes , Dirk Voigt , Andrea Aiello , J. P. Woerdman

Motivated by Hirano-Tominaga's work \cite{HT} on rings for which every element is a sum of two idempotents and by de Seguins Pazzis's results \cite{de} on decomposing every matrix over a field of positive characteristic as a sum of…

Rings and Algebras · Mathematics 2017-12-14 Gaohua Tang , Yiqiang Zhou , Huadong Su

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

Machine Learning · Computer Science 2014-11-17 Anima Anandkumar , Rong Ge , Daniel Hsu , Sham M. Kakade , Matus Telgarsky

A uniqueness theorem for an LU decomposition of a totally nonnegative matrix is obtained.

Rings and Algebras · Mathematics 2011-06-14 K R Goodearl , T H Lenagan

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…

Numerical Analysis · Mathematics 2024-07-25 Mengyu Wang , Jingchun Zhou , Hanyu Li

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…

Algebraic Geometry · Mathematics 2012-10-17 Alessandra Bernardi , Jerome Brachat , Pierre Comon , Bernard Mourrain

Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…

Information Theory · Computer Science 2022-04-15 Samet Gelincik , Philippe Mary , Anne Savard , Jean-Yves Baudais

Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are…

Exactly Solvable and Integrable Systems · Physics 2016-02-18 Blazej M. Szablikowski , Maciej Blaszak

The Mueller-Stokes formalism which governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could demand of a $4\times 4$ real matrix $M$ in order that it qualifies to be the Mueller matrix…

The vectorial evolution of polarized light interaction with a medium can reveal its microstructure and anisotropy beyond what can be obtained from scalar light interaction. Anisotropic properties (diattenuation, retardance, and…

Optics · Physics 2024-02-26 Zhineng Xie , Guowu Huang , Weihao Lin , Xin Jin , Yifan Ge , Yansen Hu , Xiafei Qian , Min Xu

Formulae for the matrix element squared of the process e gamma -> e gamma with all four particles polarized are obtained using REDUCE.

High Energy Physics - Phenomenology · Physics 2007-05-23 A. G. Grozin

We calculate all the elements of the Mueller matrix, which contains all the polarization properties of light scattered from a two-dimensional randomly rough lossy metal surface. The calculations are carried out for arbitrary angles of…

Optics · Physics 2012-11-12 Paul Anton Letnes , Alexei A. Maradudin , Tor Nordam , Ingve Simonsen

Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic waves. The polarimetric quantities that are invariant under…

Optics · Physics 2015-12-16 Jose J. Gil

This paper presents a parametrization of a degenerate density matrix. The problem needs to be approached first with a diagonalized form (the spectral representation) to deal with degeneracy. Such a form is useful for this parametrization in…

Mathematical Physics · Physics 2013-09-06 Tae-Hun Lee

V.I. Arnold [Russian Math. Surveys 26 (2) (1971) 29-43] constructed a miniversal deformation of matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced…

Representation Theory · Mathematics 2012-12-14 Andrii R. Dmytryshyn , Vyacheslav Futorny , Vladimir V. Sergeichuk

A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…

Mathematical Physics · Physics 2015-05-20 Robert P. Dahlgren

A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…

Information Theory · Computer Science 2015-03-17 Tadashi Wadayama , Manabu Hagiwara

A monolithic process is a single recursive equation with data parameters, which only uses non-determinism, action prefixing, and recursion. We present a technique that decomposes such a monolithic process into multiple processes where each…

Logic in Computer Science · Computer Science 2021-10-04 Maurice Laveaux , Tim A. C. Willemse