## 28 Citations

How to Detect and Construct N-matrices

- MathematicsArXiv
- 2020

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

- MathematicsMath. Program.
- 1993

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

- Mathematics
- 2005

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

- Mathematics, Computer ScienceLinear and Multilinear Algebra
- 2019

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

- Mathematics
- 1997

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

- Mathematics
- 2016

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

- Mathematics
- 2018

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

- Mathematics
- 2018

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.…

## References

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Some Aspects of the Theory of $PN$-Matrices

- Economics, Mathematics
- 1976

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

- Mathematics
- 1976

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

- MathematicsMath. Program.
- 1979

It is shown that for such a problem for anyq, there are either 0, 1, 2, or 3 solutions.

On global univalence theorems

- Mathematics
- 1983

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

- MathematicsMath. Program.
- 1972

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

- Mathematics
- 1972

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…