Linear operators preserving strong majorization of (0,1)-matrices

Alexander Guterman; Pavel Shteyner

doi:10.1016/j.laa.2022.10.028

Linear operators preserving strong majorization of (0,1)-matrices

Alexander Guterman, Pavel Shteyner

Department of Mathematics

Bar-Ilan University

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

Abstract

We obtain a complete characterization of linear operators that preserve strong majorization on (0,1)-matrices. To do this we introduce a new matrix invariant of combinatorial nature. We call this invariant an intersection index of a matrix and develop a method to characterize the matrix maps based on the analysis of its properties.

Original language	English
Pages (from-to)	116-150
Number of pages	35
Journal	Linear Algebra and Its Applications
Volume	658
DOIs	https://doi.org/10.1016/j.laa.2022.10.028
State	Published - 1 Feb 2023

Keywords

Linear preservers
Matrix majorization
Vector majorization

All Science Journal Classification (ASJC) codes

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

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10.1016/j.laa.2022.10.028

Cite this

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title = "Linear operators preserving strong majorization of (0,1)-matrices",

abstract = "We obtain a complete characterization of linear operators that preserve strong majorization on (0,1)-matrices. To do this we introduce a new matrix invariant of combinatorial nature. We call this invariant an intersection index of a matrix and develop a method to characterize the matrix maps based on the analysis of its properties.",

keywords = "Linear preservers, Matrix majorization, Vector majorization",

author = "Alexander Guterman and Pavel Shteyner",

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year = "2023",

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doi = "10.1016/j.laa.2022.10.028",

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T1 - Linear operators preserving strong majorization of (0,1)-matrices

AU - Guterman, Alexander

AU - Shteyner, Pavel

PY - 2023/2/1

Y1 - 2023/2/1

N2 - We obtain a complete characterization of linear operators that preserve strong majorization on (0,1)-matrices. To do this we introduce a new matrix invariant of combinatorial nature. We call this invariant an intersection index of a matrix and develop a method to characterize the matrix maps based on the analysis of its properties.

AB - We obtain a complete characterization of linear operators that preserve strong majorization on (0,1)-matrices. To do this we introduce a new matrix invariant of combinatorial nature. We call this invariant an intersection index of a matrix and develop a method to characterize the matrix maps based on the analysis of its properties.

KW - Linear preservers

KW - Matrix majorization

KW - Vector majorization

UR - http://www.scopus.com/inward/record.url?scp=85141545596&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2022.10.028

DO - 10.1016/j.laa.2022.10.028

M3 - مقالة

SN - 0024-3795

VL - 658

SP - 116

EP - 150

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Linear operators preserving strong majorization of (0,1)-matrices

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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