By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

Specially structured Linear Complementarity Problems (LCP's) and their solution by the criss{ cross method are examined in this paper. The criss{cross method is known to be nite for LCP's with positive semide nite bisymmetric matrices and with P{matrices. It is also a simple nite algorithm for oriented matroid programming problems. Recently Cottle, Pang and Venkateswaran identi ed the class of ...

The class of H-matrices, also known as Generalized Diagonally Dominant (GDD) matrices, plays an important role in many areas applied linear algebra, well a wide range applications, such dynamical analysis complex networks that arise ecology, epidemiology, infectology, neurology, engineering, economy, opinion dynamics, and other fields. To conclude the particular system is (locally) stable, it s...

In this note I give a proof of the existence of a Smith normal form for matrices with integer entries. The existence of a good basis for a lattice with a finite index sublattice is a consequence of the Smith normal form. I conclude with an easy application to toric varieties. Theorem 1. Let A be a matrix with integer entries. Then there exist integer-values invertible matrices C and B such that...

Let G be a simple undirected graph on n vertices and let S(G) be the class of real symmetric n× n matrices whose nonzero off-diagonal entries correspond exactly to the edges of G. Given 2n − 1 real numbers λ1 ≥ μ1 ≥ λ2 ≥ μ2 ≥ · · · ≥ λn−1 ≥ μn−1 ≥ λn, and a vertex v of G, the question is addressed of whether or not there exists A ∈ S(G) with eigenvalues λ1, . . . , λn such that A(v) has eigenva...

Specially structured linear complementarity problems (LCPs) and their solution by the miss-cross method are examined. The criss-cross method is known to be finite for LCPs with positive semidefinite bisymmetric matrices and with P-matrices. It is also a simple finite algorithm for oriented matroid programming problems. Recently Cottle, Pang, and Venkateswaran identified the class of (column, ro...

A matrix with positive row sums and all its off-diagonal elements bounded above by their corresponding row averages is called a B-matrix by J. M. Peña in References (SIAM J. Matrix Anal. Appl. 2001; 22:1027–1037) and (Numer. Math. 2003; 95:337–345). In this paper, it is generalized to more extended matrices—MB-matrices, which is proved to be a subclass of the class of P-matrices. Subsequently, ...