Companion factorization in the general linear group \(\mathrm{GL}(n,\mathbb C)\) and applications
type: Item
instance of: scholarly article
title: Companion factorization in the general linear group \(\mathrm{GL}(n,\mathbb C)\) and applications
zbMATH Open document ID: 1210.15014
author: Juan-Miguel Gracia
published in: Linear Algebra and its Applications
publication date: 2011-02-09T00:00:00Z
review text: Let \(M\) be an \(n\times n\) matrix over the complex numbers. The authors call \(M\) strictly nonsingular if each of its principal submatrices is nonsingular. They prove that each strictly nonsingular matrix \(M\) is a product of \(n\) companion matrices, and give simple expressions for the nonzero entries in the latter matrices in terms of certain subdeterminants of \(M\).
reviewed by: John D. Dixon
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 5848842
zbMATH Keywords: companion matrix
zbMATH Keywords: strictly nonsingular matrix
zbMATH Keywords: companion factorization
zbMATH Keywords: \(LU\) factorization
zbMATH Keywords: subdeterminants
MaRDI profile type: Publication
full work available at URL: j.laa.2010.11.016
OpenAlex ID: W2050472960
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DOI: 10.1016/J.LAA.2010.11.016
description: scientific article; zbMATH DE number 5848842