Related papers: The Cone of Mueller Matrices
Study of cosmic dust and planetary aerosols indicate that some of them contain a large number of aggregates of the size that significantly exceeds the wavelengths of the visible light. In some cases such large aggregates may dominate in…
A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $V$ such that $A = V V ^T$. In this paper, we study the CP-matrix approximation problem of projecting a matrix onto the intersection of a set…
In this diploma thesis, the calibration of the vector polarimeter POLIS will be described. The instrument is built by the Kiepenheuer-Institut fuer Sonnenphysik (Freiburg/Germany) in cooperation with the High Altitude Observatory…
The control of polarization, an essential property of light, is of wide scientific and technological interest. The general problem of generating arbitrary time-varying states of polarization (SOP) has always been mathematically formulated…
Recovering the polarized cosmic microwave background (CMB) is essential for shedding light on the exponential expansion of the very early Universe, known as cosmic inflation. Achieving this goal requires not only improved instrumental…
The polarimetry of the light scattered by planetary surfaces is a powerful tool to provide constraints on their microstructure. To improve the interpretation of polarimetric data from icy surfaces, we have developed the POLarimeter for ICE…
The state of polarization (SOP) is an inherent property of the vectorial nature of light and a crucial parameter in a wide range of remote sensing applications. Nevertheless, the SOP is rather cumbersome to probe experimentally, as…
The goal of this paper is to develop a systematic method of locating the Mueller matrices within the class of the matrices of the real group SL(4, R). The main idea is to construct the general transformation of the group SL(4, R) (whose…
We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in…
Polarization of the cosmic microwave background, though not yet detected, provides a source of information about cosmological parameters complementary to temperature fluctuations. This paper provides a complete theoretical treatment of…
The density matrix is obtained for short-wavelength photons passing through a medium. For sufficiently large thicknesses of a target this matrix is expressed by the forward scattering amplitude of a photon. For multi-GeV photons scattering…
In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity,…
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…
Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting…
In this work we present a method for generating random matrices describing electromagnetic scattering from disordered media containing dielectric particles with prescribed single particle scattering characteristics. Resulting scattering…
The objective of this manuscript is to understand the structure of an invertible linear map on the space of real symmetric matrices $\mathcal{S}^n$ that leaves invariant the closed convex cones of copositive and completely positive matrices…
In the monotone integer dualization problem, we are given two sets of vectors in an integer box such that no vector in the first set is dominated by a vector in the second. The question is to check if the two sets of vectors cover the…
We study mapping cones and their dual cones of positive maps of the n by n matrices into itself. For a natural class of cones there is a close relationship between maps in the cone, super-positive maps, and separable states. In particular…
Symmetric cones can be endowed with at least two interesting non Riemannian metrics: the Hilbert and the Thompson metrics. It is trivial that the linear maps preserving the cone are isometries for those two metrics. Oddly enough those are…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…