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

^*Corresponding author for this work

School of Mathematical Sciences

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

2 Scopus citations

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.

Original language	English
Pages (from-to)	2367-2372
Number of pages	6
Journal	Linear Algebra and Its Applications
Volume	429
Issue number	10
DOIs	https://doi.org/10.1016/j.laa.2007.06.009
State	Published - 1 Nov 2008

Keywords

Jordan canonical form
Similarity
Sparsity
Zero pattern

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10.1016/j.laa.2007.06.009

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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.",

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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

ER -

An extremal sparsity property of the Jordan canonical form

Abstract

Keywords

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