A complete and minimum set of necessary and sufficient conditions for a real 4x4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely the four conditions obtained from the non-negativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the Transmittance Condition. Using the pro...

This document consists of details to which the original submission article has made references. These include a list of symbols, some matrix identities and calculus rules, a list of VarPro derivatives, symmetry analysis of the un-regularized VarPro Gauss-Newton matrix and MTSS computation details. Symbol Meaning Rp×q The space of real matrices of size p× q S The space of symmetric real matrices...

Given the set of square matrices M ⊂ Mn+m(C) that keep the subspace W = Cnx{0} ⊂ C invariant, we obtain the implicit form of a miniversal deformation of a matrix a ∈ M, and we compute it explicitely when this matrix is marked (this is, if there is a permutation matrix p ∈ Mn+m(C) such that p−1ap is a Jordan matrix). We derive some applications to tackle the classical Carlson problem.

The question of the existence and uniqueness of an M-matrix which is a square root of an M-matrix is discussed. The results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an M-matrix.

A graph G = (V,E) is Complementary Distance Pattern Uniform if there exists M ⊂ V (G) such that fM (u) = {d(u, v) : v ∈ M}, for every u ∈ V (G)−M , is independent of the choice of u ∈ V (G)−M and the set M is called the Complementary Distance Pattern Uniform Set (CDPU set). The M -Complementary Distance Uniform Matrix (M CDU Matrix), CM (G) = [cij ] of G of order n is a p × m matrix, where m is...

This note explores sparse matrix dense matrix (SMDM) multiplications, useful in block Krylov or block Lanczos methods. SMDM computations are AU , and V A, multiplication of a large sparse matrix m × n matrix A by a matrix V of k rows of length m or a matrix U of k columns of length k, k << m, k << n . In a block Lanczos or Krylov algorithm, matrix matrix multiplications with the ”tall” U and ”w...

background: h9n2 avian influenza viruses (aiv) a have become panzootic in eurasia over the last decade and have caused several human infections in iran since 1998 and inactivated vaccine has been used in chickens to control the disease. objectives: the purpose of this study was to analyze h9n2 viruses that have infected broiler in tehran province, iran between 1998 and 2008 based on matrix gene...