A unification of some matrix factorization results
type: Item
instance of: scholarly article
title: A unification of some matrix factorization results
zbMATH Open document ID: 1179.15011
author: J. D. Botha
published in: Linear Algebra and its Applications
publication date: 2009-10-09T00:00:00Z
review text: Let \(\mathbb{F}\) be a field with at least four elements. The author shows, if \(A\in M_n(\mathbb{F})\) is a nonsingular, nonscalar matrix, then \(A\) is similar to a matrix \(B\) that has a special \(LT\) factorization with all diagonal entries except one equal to \(1\) or a factorization \(L\left[\begin{smallmatrix} U&0\\ \star&d\end{smallmatrix}\right]\) where \(L\) and \(U\) are special lower and upper triangular matrices, respectively, with all diagonal entries equal to \(1\). He uses this theorem to unify the proofs of several matrix factorization theorems.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 5612549
zbMATH Keywords: unification
zbMATH Keywords: positive definite
zbMATH Keywords: commutator
zbMATH Keywords: involution
zbMATH Keywords: finite field
zbMATH Keywords: nonderogatory
zbMATH Keywords: special \(LU\) factorization
zbMATH Keywords: special \(LT\) factorization
zbMATH Keywords: spectrum
MaRDI profile type: Publication
full work available at URL: j.laa.2009.06.006
OpenAlex ID: W1963742149
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DOI: 10.1016/J.LAA.2009.06.006
description: scientific article; zbMATH DE number 5612549