Matrix Schubert varieties are the closures of orbits B×B acting on all n×n matrices, where B is group invertible lower triangular matrices. Extending work Fulton, Knutson and Miller identified a Gröbner basis for prime ideals these varieties. They also showed that corresponding initial Stanley-Reisner shellable simplicial complexes, derived related primary decomposition in terms reduced pipe dr...

The present investigation deals with the propagation of waves in the layer of an anisotropic fibre reinforced thermoelastic solid. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitude of displacements and temperature distribution were also obtained. Finally, the numerical solution was carried out for Cobalt material...

In this work, the issue of computing a real logarithm of a real matrix is addressed. After a brief review of some known methods, more attention is paid to three methods: (i) Padé approximation techniques, (ii) Newton’s method, and (iii) a series expansion method. Newton’s method has not been previously treated in the literature; we address commutativity issues, and simplify the algorithmic form...

This paper shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new skew centrosymmetric matrix is also discussed. The application of the properties of centrosymmetric and skew centrosymmetric matrix can reduce the computational...

First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also determine minimal structured perturbations for which approximate eigenelements are exact eigenelements of the perturbed polynomials. Next, we analyze the effe...

In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that, for a fixed finite field F, any infinite sequenceM1,M2, . . . of (skew) symmetric matrices over F of bounded F-rank-width has a pair i < j, such that Mi is isomorphic to a principal submatrix of a principal pivot transform of Mj . We generalise this result to σ-symmetric matrices ...

We study the range S(A) := {xT Ay : x, y are orthonormal in Rn}, where A is an n×n complex skew symmetric matrix. It is a compact convex set. Power inequality s(A) ≤ s(A), k ∈ N, for the radius s(A) := maxξ∈S(A) |ξ| is proved. When n = 3, 4, 5, 6, relations between S(A) and the classical numerical range and the k-numerical range are given. Axiomatic characterization of S(A) is given. Sharp poin...

Two matrix vector spaces V,W⊂Cn×n are said to be equivalent if SVR=W for some nonsingular S and R. These congruent R=ST. We prove that all matrices in V W symmetric, or skew-symmetric, then only they equivalent. Let F:U×…×U→V G:U′×…×U′→V′ symmetric skew-symmetric k-linear maps over C. If there exists a set of linear bijections φ1,…,φk:U→U′ ψ:V→V′ transforms F G, such with φ1=…=φk.

The contragredient transformation A 7→ PAP, B 7→ PBP of two matrices A,B effects simultaneous similarity transformations of the products AB and BA. This work provides structured canonical forms under this transformation for symmetric or skew-symmetric A,B. As an application, these forms are used to study the quadratic matrix equation XAX = B, where both A,B are skew-symmetric or symmetric matri...