Eigenvalue continuity and Gersgorin's theorem

Chi-Kwong Li; Fuzhen Zhang

doi:10.13001/ela.2019.5179

Eigenvalue continuity and Gersgorin's theorem

Chi-Kwong Li
, Fuzhen Zhang

Department of Mathematics

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

Abstract

Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Geršgorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified.

Original language	American English
Pages (from-to)	619-625
Number of pages	7
Journal	Journal of Linear Algebra
Volume	35
DOIs	https://doi.org/10.13001/ela.2019.5179
State	Published - Dec 9 2019

Keywords

Eigenvalue continuity
Gerˇsgorin disk theorem
Root continuity

Disciplines

Mathematics

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10.13001/ela.2019.5179

Eigenvalue continuity and Gersgorins theoremFinal published version, 392 KBLicense: Unspecified

Cite this

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title = "Eigenvalue continuity and Gersgorin's theorem",

abstract = "Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Ger{\v s}gorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified.",

keywords = "Eigenvalue continuity, Gerˇsgorin disk theorem, Root continuity",

author = "Chi-Kwong Li and Fuzhen Zhang",

year = "2019",

month = dec,

day = "9",

doi = "10.13001/ela.2019.5179",

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journal = "Journal of Linear Algebra",

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AU - Li, Chi-Kwong

AU - Zhang, Fuzhen

PY - 2019/12/9

Y1 - 2019/12/9

N2 - Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Geršgorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified.

AB - Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Geršgorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified.

KW - Eigenvalue continuity

KW - Gerˇsgorin disk theorem

KW - Root continuity

UR - https://nsuworks.nova.edu/math_facarticles/304

UR - https://www.mendeley.com/catalogue/612cb445-2833-3bdb-b492-acb1d88adf8a/

U2 - 10.13001/ela.2019.5179

DO - 10.13001/ela.2019.5179

M3 - Article

SN - 1081-3810

VL - 35

SP - 619

EP - 625

JO - Journal of Linear Algebra

JF - Journal of Linear Algebra

ER -

Eigenvalue continuity and Gersgorin's theorem

Abstract

Keywords

Disciplines

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