Extremal sparsity of the companion matrix of a polynomial

Chao Ma; Xingzhi Zhan

doi:10.1016/j.laa.2012.08.017

Extremal sparsity of the companion matrix of a polynomial

Chao Ma
, Xingzhi Zhan^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Let C be the companion matrix of a monic polynomial p over a field F. We prove that if A is a matrix whose entries are rational functions of the coefficients of p over F and whose characteristic polynomial is p, then A has at least as many nonzero entries as C.

Original language	English
Pages (from-to)	621-625
Number of pages	5
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2012.08.017
State	Published - 1 Jan 2013

Keywords

Companion matrix
Polynomial
Spanning branching
Sparsity
Transcendence degree

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title = "Extremal sparsity of the companion matrix of a polynomial",

abstract = "Let C be the companion matrix of a monic polynomial p over a field F. We prove that if A is a matrix whose entries are rational functions of the coefficients of p over F and whose characteristic polynomial is p, then A has at least as many nonzero entries as C.",

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author = "Chao Ma and Xingzhi Zhan",

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AU - Ma, Chao

AU - Zhan, Xingzhi

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Let C be the companion matrix of a monic polynomial p over a field F. We prove that if A is a matrix whose entries are rational functions of the coefficients of p over F and whose characteristic polynomial is p, then A has at least as many nonzero entries as C.

AB - Let C be the companion matrix of a monic polynomial p over a field F. We prove that if A is a matrix whose entries are rational functions of the coefficients of p over F and whose characteristic polynomial is p, then A has at least as many nonzero entries as C.

KW - Companion matrix

KW - Polynomial

KW - Spanning branching

KW - Sparsity

KW - Transcendence degree

UR - https://www.scopus.com/pages/publications/84869089077

U2 - 10.1016/j.laa.2012.08.017

DO - 10.1016/j.laa.2012.08.017

M3 - 文章

AN - SCOPUS:84869089077

SN - 0024-3795

VL - 438

SP - 621

EP - 625

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Extremal sparsity of the companion matrix of a polynomial

Abstract

Keywords

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