Bidiagonal decompositions of oscillating systems of vectors
type: Item
instance of: scholarly article
title: Bidiagonal decompositions of oscillating systems of vectors
zbMATH Open document ID: 1143.15021
author: Froilán M. Dopico
author: Plamen Koev
published in: Linear Algebra and its Applications
publication date: 2008-05-15T00:00:00Z
review text: The authors obtain necessary and sufficient conditions for a matrix \(V\) to be a matrix of eigenvectors of a totally positive matrix. Namely, this is the case if and only if \(V\) and \(V^{-T}\) are lowerly totally positive. These conditions translate into easy requirements on the parameters in the bidiagonal decompositions of \(V\) and \(V^{-T}\). By using these decompositions they give elementary proofs of the oscillating properties of \(V\). In particular, of the fact that the \(j\)th column of \(V\) has \(j-1\) changes of sign. The results include the fact that the \(Q\) matrix in a QR decomposition of a totally positive matrix belongs to the above class.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 5275744
zbMATH Keywords: totally positive matrix
zbMATH Keywords: variation diminishing property
zbMATH Keywords: eigenvectors
reviewed by: Andreas Arvanitoyeorgos
describes a project that uses: TNTool
MaRDI profile type: Publication
full work available at URL: j.laa.2007.12.002
OpenAlex ID: W2061064212
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DOI: 10.1016/J.LAA.2007.12.002
description: scientific article; zbMATH DE number 5275744