In this work we propose a general framework for the structured perturbation analysis of several classes of structured matrix polynomials in homogeneous form, including complex symmetric, skew-symmetric, even and odd matrix polynomials. We introduce structured backward errors for approximate eigenvalues and eigenvectors and we construct minimal structured perturbations such that an approximate e...

let $g$ be a simple graph‎, ‎and $g^{sigma}$‎ ‎be an oriented graph of $g$ with the orientation ‎$sigma$ and skew-adjacency matrix $s(g^{sigma})$‎. ‎the $k-$th skew spectral‎ ‎moment of $g^{sigma}$‎, ‎denoted by‎ ‎$t_k(g^{sigma})$‎, ‎is defined as $sum_{i=1}^{n}( ‎‎‎lambda_{i})^{k}$‎, ‎where $lambda_{1}‎, ‎lambda_{2},cdots‎, ‎lambda_{n}$ are the eigenvalues of $g^{sigma}$‎. ‎suppose‎ ‎$g^{sigma...

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

Let G be a graph with adjacency matrix A and let F be a field. An F-matrix Q is a support matrix of G if A = [Q ̸=O], the zero-nonzero pattern of Q. If G has an invertible skew-symmetric support F-matrix S, the S-dual G of G is defined as the graph with adjacency matrix [S−1 ̸= O]. An analogous adjacency matrix dual, G has been examined in the literature for those bipartite graphs G with unique p...

Based on the results obtained in [Hucht, J. Phys. A: Math. Theor. 50, 065201 (2017)], we show that partition function of anisotropic square lattice Ising model $L \times M$ rectangle, with open boundary conditions both directions, is given by determinant a $M/2 M/2$ Hankel matrix, equivalently can be written as Pfaffian skew-symmetric $M Toeplitz matrix. The $M-1$ independent matrix elements ma...

In this paper we generalize the known De Smet, Dillen, Verstraelen and Vrancken (DDVV)-type inequalities for real (skew-)symmetric complex (skew-)Hermitian matrices to arbitrary real, quaternionic matrices. Inspired by Erdős-Mordell inequality, establish DDVV-type in subspaces spanned a Clifford system or algebra. We also Böttcher-Wenzel inequality

We study the problem of feedback control for skew-symmetric and skewHamiltonian transfer functions using skew-symmetric controllers. This extends work of Helmke, et al., who studied static symmetric feedback control of symmetric and Hamiltonian linear systems. We identify spaces of linear systems with symmetry as natural subvarieties of the moduli space of rational curves in a Grassmannian, giv...

In this note, we consider the problem of computing the exponential of a real matrix. It is shown that if A is a real n × n matrix and A can be diagonalized over C, then there is a formula for computing e involving only real matrices. When A is a skew symmetric matrix, the formula reduces to the generalization of Rodrigues’s formula given in Gallier and Xu [1].

In present study is concerned with the propagation of axisymmetric vibrations in a homogenous isotropic micropolar thermoelastic cubic crystal plate bordered with layers or half spaces of inviscid liquid subjected to stress free boundary conditions in context of Lord and Shulman (L-S) and Green and Lindsay (G-L) theories of thermoelasticity. The secular equations for symmetric and skew-symmetri...