Geršgorin discs revisited

Miroslav Fiedler; Frank J. Hall; Rachid Marsli

doi:10.1016/j.laa.2012.07.027

Geršgorin discs revisited

Miroslav Fiedler^*, Frank J. Hall, Rachid Marsli

^*Corresponding author for this work

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

6 Scopus citations

Abstract

Let k, r, t be positive integers with k≤r≤t. For such a given triple of integers, we prove that there is a t × t complex matrix A and an eigenvalue λ of A such that λ has geometric multiplicity k and algebraic multiplicity t, and λ is in precisely r Geršgorin discs of A. Some examples and related results are also provided.

Original language	English
Pages (from-to)	598-603
Number of pages	6
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2012.07.027
State	Published - 1 Jan 2013
Externally published	Yes

Keywords

Algebraic multiplicity
Geometric multiplicity
Geršgorin disc

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2012.07.027

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title = "Ger{\v s}gorin discs revisited",

abstract = "Let k, r, t be positive integers with k≤r≤t. For such a given triple of integers, we prove that there is a t × t complex matrix A and an eigenvalue λ of A such that λ has geometric multiplicity k and algebraic multiplicity t, and λ is in precisely r Ger{\v s}gorin discs of A. Some examples and related results are also provided.",

keywords = "Algebraic multiplicity, Geometric multiplicity, Ger{\v s}gorin disc",

author = "Miroslav Fiedler and Hall, \{Frank J.\} and Rachid Marsli",

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T1 - Geršgorin discs revisited

AU - Fiedler, Miroslav

AU - Hall, Frank J.

AU - Marsli, Rachid

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Let k, r, t be positive integers with k≤r≤t. For such a given triple of integers, we prove that there is a t × t complex matrix A and an eigenvalue λ of A such that λ has geometric multiplicity k and algebraic multiplicity t, and λ is in precisely r Geršgorin discs of A. Some examples and related results are also provided.

AB - Let k, r, t be positive integers with k≤r≤t. For such a given triple of integers, we prove that there is a t × t complex matrix A and an eigenvalue λ of A such that λ has geometric multiplicity k and algebraic multiplicity t, and λ is in precisely r Geršgorin discs of A. Some examples and related results are also provided.

KW - Algebraic multiplicity

KW - Geometric multiplicity

KW - Geršgorin disc

UR - https://www.scopus.com/pages/publications/84869087148

U2 - 10.1016/j.laa.2012.07.027

DO - 10.1016/j.laa.2012.07.027

M3 - Article

AN - SCOPUS:84869087148

SN - 0024-3795

VL - 438

SP - 598

EP - 603

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Geršgorin discs revisited

Abstract

Keywords

ASJC Scopus subject areas

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