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^*

^*此作品的通讯作者

数学科学学院

East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	621-625
页数	5
期刊	Linear Algebra and Its Applications
卷	438
期	1
DOI	https://doi.org/10.1016/j.laa.2012.08.017
出版状态	已出版 - 1 1月 2013

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10.1016/j.laa.2012.08.017

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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

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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

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

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Extremal sparsity of the companion matrix of a polynomial

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