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

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

1 Scopus citations

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

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Linear preservers
Matrix majorization
Vector majorization

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10.1016/j.laa.2022.10.028

Cite this

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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.",

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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

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

Abstract

Bibliographical note

Keywords

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