Every unit matrix is a LULU
type: Item
instance of: scholarly article
title: Every unit matrix is a LULU
zbMATH Open document ID: 0918.15004
DOI: 10.1016/S0024-3795(96)00598-8
author: Gilbert Strang
published in: Linear Algebra and its Applications
publication date: 1999-08-19T00:00:00Z
review text: This paper is devoted to prove that every unit matrix \(A\) (i.e. every matrix with determinant one) has a factorization of the form \(A=L_0 U_0 L_1 U_1\), where the four matrices are triangular with ones on their diagonal (\(L_i\) are lower triangular, and \(U_i\) are upper triangular). The paper should be read in connection to \textit{T. Toffoli}'s paper [ibid. 259, 31-38 (1997; Zbl 0893.15004)] where a related result, motivated with examples from computer graphics, is stated. In the paper under review, the author proves the existence of a factorization as a product of four triangular matrices for every unit matrix (not almost every). In addition, it should be mentioned that the problem of finding an efficient method to construct the factorization (``a minimal adjustment'' in the author's words) remains open.
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1076376
zbMATH Keywords: unit matrix
zbMATH Keywords: factorization
zbMATH Keywords: triangular matrices
reviewed by: J. Rafael Sendra
MaRDI profile type: Publication
cites work: Almost every unit matrix is a \(ULU\)
description: scientific article; zbMATH DE number 1076376