Extremal sparsity of the companion matrix of a polynomial
type: Item
instance of: scholarly article
title: Extremal sparsity of the companion matrix of a polynomial
zbMATH Open document ID: 1269.15007
author: Chao Ma
author: Xingzhi Zhan
published in: Linear Algebra and its Applications
publication date: 2013-01-21T00:00:00Z
review text: Let \(C\) be the companion matrix of a monic polynomial \(p\) over a field \(\mathbb F\). The authors prove that if \(A\) is a matrix whose entries are rational functions of the coefficients of \(p\) over \(\mathbb F\) and whose characteristic polynomial is \(p\), then \(A\) has at least as many nonzero entries as \(C\). In other words, the companion matrix is the sparsest matrix of the mentioned set of matrices \(A\).
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 11C20
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 6127366
zbMATH Keywords: polynomial
zbMATH Keywords: companion matrix
zbMATH Keywords: sparsity
zbMATH Keywords: spanning branching
zbMATH Keywords: transcendence degree
MaRDI profile type: Publication
full work available at URL: j.laa.2012.08.017
OpenAlex ID: W1985103827
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DOI: 10.1016/J.LAA.2012.08.017
description: scientific article; zbMATH DE number 6127366