Almost N-matrices and linear complementarity

  title={Almost N-matrices and linear complementarity},
  author={Czeslaw Olech and Thiruvenkatachari Parthasarathy and G. Ravindran},
  journal={Linear Algebra and its Applications},
How to Detect and Construct N-matrices
An O(2^n) test to detect whether or not a given matrix is an N-matrix, and a characterization of N-Matrices, leading to the recursive construction of every N- matrix are provided.
Ky Fan's N-matrices and linear complementarity problems
It is shown that if A is a Z-matrix, then A is an F-matrices if and only if LCP(q, A) has exactly two solutions for anyq⩾0,q≠0, and has at most two solutionsFor any otherq.
On almost type classes of matrices with Q-property
In this article, we introduce a new matrix class almost (a subclass of almost N 0-matrices which are obtained as a limit of a sequence of almost N-matrices) and obtain a sufficient condition for this
More on hidden Z-matrices and linear complementarity problem
It is shown that for a non-degenerate feasible basis, linear complementarity problem with hidden Z-matrix has unique non- Degenerate solution under some assumptions.
Completely Mixed Games And Real Jacobian Conjecture
In this paper, we consider Cubic Linear Mapping F : Rn → Rn, where Fi = Xi + (AX) i 3 , X ∈ Rn, i = 1,2,…n A is an n x n matrix and study the injectivity of F when A is a P0 matrix or when A is a Z
Isotone projection cones and Q-matrices
Proper cones with the property that the projection onto them is isotone with respect to the order they induce are called isotone projection cones. Isotone projection cones and their extensions have
New Contributions to Semipositive and Minimally Semipositive Matrices
Semipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is
On Linear Complementarity Problem with Hidden Z-Matrix
In this article we study linear complementarity problem with hidden Z-matrix. We extend the results of Fiedler and Pták for the linear system in complementarity problem using game theoretic approach.


Some Aspects of the Theory of $PN$-Matrices
A matrix is a $PN$-matrix if its principal minors of even order are negative and its principal minors of odd order greater than or equal to three are all positive. Such matrices have been studied by
Some Perturbation Theorems for Q-Matrices
Given a real $n \times n$ matrix M and vector q, the linear complementarily problem is to find vectors w and z such that $w - Mz = q$, $w\geqq 0$, $z\geqq 0$, $w^t z = 0$. M is nondegenerate if all
On the number of solutions to a class of linear complementarity problems
It is shown that for such a problem for anyq, there are either 0, 1, 2, or 3 solutions.
On global univalence theorems
Preliminaries and statement of the problem.- P-matrices and N-matrices.- Fundamental global univalence results of Gale-Nikaido-Inada.- Global homeomorphisms between finite dimensional spaces.-
The complementarity problem
Several existence theorems are given under various conditions on the mapF, which cover the cases whenF is nonlinear nondifferentiable, nonlinear but differentiable, and affine.
A Characterization of the Constant Parity Property of the Number of Solutions to the Linear Complementarity Problem
We consider the linear complementarily problem: Given an $m \times m$ matrix M and a real m-vector q, find real m-vectors x and y which solve (i) $x = My + q,x\geqq 0,y\geqq 0$, (ii) $x^T y = 0$. In