On the necessity and sufficiency of \(PLUS\) factorizations
type: Item
instance of: scholarly article
title: On the necessity and sufficiency of \(PLUS\) factorizations
zbMATH Open document ID: 1071.15012
author: Yiyuan She
author: Pengwei Hao
published in: Linear Algebra and its Applications
publication date: 2005-06-01T00:00:00Z
review text: A \(PLUS\) factorization for an arbitrary nonsingular \(n\times n\) matrix \(A\) has the form \(A=PLUS\), where \(P\) is a permutation matrix, \(L\) is a unit lower triangular matrix, \(U\) is an upper triangular matrix whose diagonal entries are prescribed as long as the determinant is equal to that of \(A\) up to a possible sign adjustment, and \(S\) is a unit lower triangular matrix of which all but \(n-1\) off-diagonal entries are zeros and the positions of those \(n-1\) entries are also flexibly customizable. The authors show that the necessary condition for the existence of a \(PLUS\) factorization of a matrix \(A\) as given by \textit{P. Hao} [ibid. 382, 135--154 (2004; Zbl 1050.15012)] is not sufficient and they find a sufficient condition for such a factorization.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 2173024
zbMATH Keywords: triangular factorization
zbMATH Keywords: reversible integer transform
zbMATH Keywords: transform by shears
zbMATH Keywords: PLUS factorization
MaRDI profile type: Publication
Wikidata QID: Q114152473
full work available at URL: j.laa.2004.11.024
OpenAlex ID: W2153358218
cites work: Factoring wavelet transforms into lifting steps
cites work: Matrix factorizations for reversible integer mapping
cites work: Customizable triangular factorizations of matrices
cites work: Products of three triangular matrices
cites work: Block TERM factorization of block matrices
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DOI: 10.1016/J.LAA.2004.11.024
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description: scientific article; zbMATH DE number 2173024