More On Hidden $Z$-Matrices and Linear Complementarity Problem
R. Jana, A. Dutta, A. K. Das
TL;DR
This paper investigates the properties of hidden Z-matrices within linear complementarity problems, extending existing results and establishing conditions for unique solutions using a game-theoretic approach.
Contribution
It extends prior work on hidden Z-matrices by applying a game-theoretic approach and establishing conditions for unique solutions in non-degenerate cases.
Findings
Extended results of Fiedler and Ptak for linear systems
Established conditions for unique solutions with hidden Z-matrices
Analyzed singular hidden Z-matrices
Abstract
In this article we study linear complementarity problem with hidden -matrix. We extend the results of Fiedler and Pt{\'a}k for the linear system in complementarity problem using game theoretic approach. We establish a result related to singular hidden -matrix. We show that for a non-degenerate feasible basis, linear complementarity problem with hidden -matrix has unique non-degenerate solution under some assumptions. The purpose of this paper is to study some properties of hidden -matrix.
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