\(5 \times 5\) completely positive matrices
type: Item
instance of: scholarly article
title: \(5 \times 5\) completely positive matrices
zbMATH Open document ID: 1067.15019
author: A. Berman
author: Changqing Xu
published in: Linear Algebra and its Applications
publication date: 2005-01-11T00:00:00Z
review text: A matrix is said to be completely positive if \(A=BB^T\) where \(B\) is nonnegative (entrywise); this implies double nonnegativity, that is, both entrywise nonnegativity and positive semidefiniteness. This paper gives a list of sufficient conditions for the converse for \(5\times 5\) matrices, which involve Schur complements. Two conjectures are stated which would complete the characterization of \(5\times 5\) completely positive matrices.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 2126342
zbMATH Keywords: completely positive matrix
zbMATH Keywords: doubly nonnegative matrix
zbMATH Keywords: factorization
zbMATH Keywords: Schur complements
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
full work available at URL: j.laa.2004.07.016
OpenAlex ID: W2059881830
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DOI: 10.1016/J.LAA.2004.07.016
description: scientific article; zbMATH DE number 2126342