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

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 o...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 658; pp. 116 - 150
Main Authors Guterman, Alexander, Shteyner, Pavel
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2023
Subjects
Linear preservers
Matrix majorization
Vector majorization
Matrix majorization
15B51
Vector majorization
06A06
Linear preservers
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2022.10.028