Generalized \(P_ 0\)- and \(Z\)-matrices
type: Item
instance of: scholarly article
title: Generalized \(P_ 0\)- and \(Z\)-matrices
zbMATH Open document ID: 0792.15010
DOI: 10.1016/0024-3795(93)90262-M
author: Aniekan A. Ebiefung
author: Michael M. Kostreva
published in: Linear Algebra and its Applications
publication date: 1994-08-07T00:00:00Z
review text: The study of linear complementarity problems often relies on the structure of the associated matrix. The same can be expected of the generalized problem. In this paper, the authors characterize the vertical block \(P_ 0\)- and \(Z\)-matrix classes. These characterizations include extensions of some of the classical results of \textit{M. Fiedler} and \textit{V. Pták} [Czechosl. Math. J. 12(87), 382-400 (1962; Zbl 0131.248); Numer. Math. 9, 163-172 (1966; Zbl 0148.258)] for the square \(P_ 0\)- and \(Z\)-matrices. The choice of these two matrix classes relates to their potential to further advance the application areas of linear algebra. The paper is organized as follows. In Section 2, the authors give definitions and notation needed for the development. Sections 3 and 4 are devoted to mathematical properties and characterizations of the \(Z\) and \(P_ 0\) classes, respectively. Section 5 is a brief conclusion.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 519695
zbMATH Keywords: \(P\)-matrix
zbMATH Keywords: \(M\)-matrix
zbMATH Keywords: \(Z\)-matrices
zbMATH Keywords: linear complementarity problems
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
cites work: A generalization of the linear complementarity problem
cites work: Q4003375
cites work: Optimal Solution of a Dynamic Leontief Model with Substitution
cites work: The Linear Complementarity Problem
cites work: The generalized Leontief input-output model and its application to the choice of new technology
cites work: NOTE ON M-MATRICES
cites work: Q5340130
cites work: Some generalizations of positive definiteness and monotonicity
cites work: Linear complementarity problems and characterizations of Minkowski matrices
cites work: Q5635264
cites work: Q4182279
cites work: Linear complementarity problems solvable by A single linear program
cites work: Q4039868
cites work: Determinanten mit überwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen
cites work: Existence and uniqueness of solutions for the generalized linear complementarity problem
cites work: An Application of Z-Matrices to a Class of Resource Allocation Problems
description: scientific article; zbMATH DE number 519695