Additive maps preserving rank-bounded sets of matrices

E. Akhmedova; A. Guterman; I. Spiridonov

doi:https://doi.org/10.1016/j.laa.2025.01.018

Additive maps preserving rank-bounded sets of matrices

E. Akhmedova, A. Guterman, I. Spiridonov

Department of Mathematics

Bar-Ilan University

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

Abstract

Let 2≤k≤n be integers and Mat_n(F) be the linear space of n×n matrices over a field F of characteristic different from 2. Denote by Γ^≥k the set of matrices in Mat_n(F) of rank greater than or equal to k. The main goal of the present paper is to obtain a characterization of additive maps f:Mat_n(F)→Mat_n(F) satisfying f(Γ^≥k)=Γ^≥k with either n<2k−2 or F has characteristic char(F)=0 or char(F)≥k.

Original language	English
Pages (from-to)	331-341
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	709
DOIs	https://doi.org/10.1016/j.laa.2025.01.018
State	Published - 15 Mar 2025

Keywords

Additive map
Preservers
Rank

All Science Journal Classification (ASJC) codes

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

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https://doi.org/10.1016/j.laa.2025.01.018

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title = "Additive maps preserving rank-bounded sets of matrices",

abstract = "Let 2≤k≤n be integers and Matn(F) be the linear space of n×n matrices over a field F of characteristic different from 2. Denote by Γ≥k the set of matrices in Matn(F) of rank greater than or equal to k. The main goal of the present paper is to obtain a characterization of additive maps f:Matn(F)→Matn(F) satisfying f(Γ≥k)=Γ≥k with either n<2k−2 or F has characteristic char(F)=0 or char(F)≥k.",

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author = "E. Akhmedova and A. Guterman and I. Spiridonov",

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TY - JOUR

T1 - Additive maps preserving rank-bounded sets of matrices

AU - Akhmedova, E.

AU - Guterman, A.

AU - Spiridonov, I.

PY - 2025/3/15

Y1 - 2025/3/15

N2 - Let 2≤k≤n be integers and Matn(F) be the linear space of n×n matrices over a field F of characteristic different from 2. Denote by Γ≥k the set of matrices in Matn(F) of rank greater than or equal to k. The main goal of the present paper is to obtain a characterization of additive maps f:Matn(F)→Matn(F) satisfying f(Γ≥k)=Γ≥k with either n<2k−2 or F has characteristic char(F)=0 or char(F)≥k.

AB - Let 2≤k≤n be integers and Matn(F) be the linear space of n×n matrices over a field F of characteristic different from 2. Denote by Γ≥k the set of matrices in Matn(F) of rank greater than or equal to k. The main goal of the present paper is to obtain a characterization of additive maps f:Matn(F)→Matn(F) satisfying f(Γ≥k)=Γ≥k with either n<2k−2 or F has characteristic char(F)=0 or char(F)≥k.

KW - Additive map

KW - Preservers

KW - Rank

UR - http://www.scopus.com/inward/record.url?scp=85215591009&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.laa.2025.01.018

DO - https://doi.org/10.1016/j.laa.2025.01.018

M3 - مقالة

SN - 0024-3795

VL - 709

SP - 331

EP - 341

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Additive maps preserving rank-bounded sets of matrices

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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