Mixed dominating matrices
type: Item
instance of: scholarly article
title: Mixed dominating matrices
zbMATH Open document ID: 0889.15020
DOI: 10.1016/S0024-3795(97)00239-5
author: Klaus G. Fischer
author: Jay Shapiro
author: Walter Morris
published in: Linear Algebra and its Applications
publication date: 1998-06-02T00:00:00Z
review text: The authors characterize matrices for which the set of supports of nonnegative vectors in the null space can be determined by the signs of the matrix. This characterization is in terms of mixed dominating matrices, which are defined by the nonexistence of square submatrices that have nonzeros of opposite sign in each row. The class of mixed dominating matrices is contained in the class of L-matrices from the theory of sign-solvability, and generalizes the class of S-matrices. The authors give a polynomial-time algorithm to decide if a matrix is mixed dominating. They derive combinatorial conditions on the face lattice of a Gale transform of a matrix in this class. Theorem 2.9 is the key to a polynomial-time for recognizing mixed dominating matrices.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 1109500
zbMATH Keywords: nonnegative vectors
zbMATH Keywords: mixed dominating matrices
zbMATH Keywords: L-matrices
zbMATH Keywords: sign-solvability
zbMATH Keywords: S-matrices
zbMATH Keywords: polynomial-time algorithm
zbMATH Keywords: Gale transform
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1109500