Full rank factorization in echelon form of totally nonpositive (negative) rectangular matrices
type: Item
instance of: scholarly article
title: Full rank factorization in echelon form of totally nonpositive (negative) rectangular matrices
zbMATH Open document ID: 1178.15020
author: Rafael Cantó
author: Beatriz Ricarte
author: Ana M. Urbano
published in: Linear Algebra and its Applications
publication date: 2009-10-14T00:00:00Z
review text: A real matrix is called totally nonpositive (negative) if every minor is nonpositive (negative). Motivated by the work of \textit{M. Gasca} and \textit{J. M. Peña} [Linear Algebra Appl. 165, 25--44 (1992; Zbl 0749.15010) and SIAM J. Matrix Anal. Appl. 25, No.~4, 986--994 (2004; Zbl 1066.65032)] on a variant of the Neville elimination process (the so-called quasi-Neville), the authors derive a characterization of totally negative matrices in terms of their full rank factorization in echelon form. Moreover, they use this factorization to reduce the number of minors to be checked in order to decide the totally negativity of rectangular matrices. The totally nonpositive case is considered under some restrictions. Several examples are considered.
reviewed by: C. M.da Fonseca
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 5614899
zbMATH Keywords: totally positive and strictly totally positive matrices
zbMATH Keywords: totally nonpositive and totally negative matrices
zbMATH Keywords: full rank factorization
zbMATH Keywords: Neville elimination
MaRDI profile type: Publication
full work available at URL: j.laa.2009.07.020
OpenAlex ID: W2050515752
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DOI: 10.1016/J.LAA.2009.07.020
description: scientific article; zbMATH DE number 5614899