An extremal sparsity property of the Jordan canonical form

Richard A. Brualdi; Pei Pei; Xingzhi Zhan

doi:10.1016/j.laa.2007.06.009

An extremal sparsity property of the Jordan canonical form

Richard A. Brualdi^*
, Pei Pei
, Xingzhi Zhan

^*此作品的通讯作者

数学科学学院

University of Wisconsin-Madison
East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

We prove that among all the matrices that are similar to a given square complex matrix, the Jordan canonical form has the largest number of off-diagonal zero entries. We also characterize those matrices that attain this largest number.

源语言	英语
页（从-至）	2367-2372
页数	6
期刊	Linear Algebra and Its Applications
卷	429
期	10
DOI	https://doi.org/10.1016/j.laa.2007.06.009
出版状态	已出版 - 1 11月 2008

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title = "An extremal sparsity property of the Jordan canonical form",

abstract = "We prove that among all the matrices that are similar to a given square complex matrix, the Jordan canonical form has the largest number of off-diagonal zero entries. We also characterize those matrices that attain this largest number.",

keywords = "Jordan canonical form, Similarity, Sparsity, Zero pattern",

author = "Brualdi, \{Richard A.\} and Pei Pei and Xingzhi Zhan",

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T1 - An extremal sparsity property of the Jordan canonical form

AU - Brualdi, Richard A.

AU - Pei, Pei

AU - Zhan, Xingzhi

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N2 - We prove that among all the matrices that are similar to a given square complex matrix, the Jordan canonical form has the largest number of off-diagonal zero entries. We also characterize those matrices that attain this largest number.

AB - We prove that among all the matrices that are similar to a given square complex matrix, the Jordan canonical form has the largest number of off-diagonal zero entries. We also characterize those matrices that attain this largest number.

KW - Jordan canonical form

KW - Similarity

KW - Sparsity

KW - Zero pattern

UR - https://www.scopus.com/pages/publications/51349137901

U2 - 10.1016/j.laa.2007.06.009

DO - 10.1016/j.laa.2007.06.009

M3 - 文章

AN - SCOPUS:51349137901

SN - 0024-3795

VL - 429

SP - 2367

EP - 2372

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 10

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An extremal sparsity property of the Jordan canonical form

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