Preservers of eigenvalue inclusion sets of matrix products

Virginia Forstall; Aaron Herman; Chi Kwong Li; Nung Sing Sze; Vincent Yannello

doi:10.1016/j.laa.2010.08.016

Preservers of eigenvalue inclusion sets of matrix products

Virginia Forstall
, Aaron Herman
, Chi Kwong Li
, Nung Sing Sze
, Vincent Yannello

Research output: Journal article publication › Journal article › Academic research › peer-review

4 Citations (Scopus)

Abstract

For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the union of Cassini ovals, and the Ostrowski's set. Characterization is obtained for maps Φ on n×n matrices satisfying S(Φ(A)Φ(B))=S(AB) for all matrices A and B.

Original language	English
Pages (from-to)	285-293
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	434
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2010.08.016
Publication status	Published - 1 Jan 2011

Keywords

Brauer's set
Cassini ovals
Gershgorin regions
Ostrowski set
Preservers

ASJC Scopus subject areas

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

More information

10.1016/j.laa.2010.08.016

Cite this

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abstract = "For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the union of Cassini ovals, and the Ostrowski's set. Characterization is obtained for maps Φ on n×n matrices satisfying S(Φ(A)Φ(B))=S(AB) for all matrices A and B.",

keywords = "Brauer's set, Cassini ovals, Gershgorin regions, Ostrowski set, Preservers",

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AU - Forstall, Virginia

AU - Herman, Aaron

AU - Li, Chi Kwong

AU - Sze, Nung Sing

AU - Yannello, Vincent

PY - 2011/1/1

Y1 - 2011/1/1

N2 - For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the union of Cassini ovals, and the Ostrowski's set. Characterization is obtained for maps Φ on n×n matrices satisfying S(Φ(A)Φ(B))=S(AB) for all matrices A and B.

AB - For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the union of Cassini ovals, and the Ostrowski's set. Characterization is obtained for maps Φ on n×n matrices satisfying S(Φ(A)Φ(B))=S(AB) for all matrices A and B.

KW - Brauer's set

KW - Cassini ovals

KW - Gershgorin regions

KW - Ostrowski set

KW - Preservers

UR - https://www.scopus.com/pages/publications/78049430023

U2 - 10.1016/j.laa.2010.08.016

DO - 10.1016/j.laa.2010.08.016

M3 - Journal article

SN - 0024-3795

VL - 434

SP - 285

EP - 293

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Preservers of eigenvalue inclusion sets of matrix products

Abstract

Keywords

ASJC Scopus subject areas

More information

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