Automorphisms of the total digraph for the ring of square matrices over a field

C. Costara; A. E. Guterman; A. M. Maksaev; V. V. Promyslov

doi:10.1016/j.laa.2023.03.007

Automorphisms of the total digraph for the ring of square matrices over a field

C. Costara, A. E. Guterman, A. M. Maksaev, V. V. Promyslov

Department of Mathematics

Bar-Ilan University

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

Abstract

In this paper, we characterize the automorphisms of the total graph for the ring M_n of matrices of order n≥2 over any field with at least 3 elements. To do this, we apply the technique of maps preserving matrix invariants; in particular, as an intermediate step, we characterize pairs of surjective maps φ₁,φ₂:M_n→M_n such that A+B is singular if and only if φ₁(A)+φ₂(B) is singular.

Original language	English
Pages (from-to)	129-143
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	666
DOIs	https://doi.org/10.1016/j.laa.2023.03.007
State	Published - 1 Jun 2023

Keywords

Automorphisms of graphs
Determinant
Nonlinear preserver

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.2023.03.007

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abstract = "In this paper, we characterize the automorphisms of the total graph for the ring Mn of matrices of order n≥2 over any field with at least 3 elements. To do this, we apply the technique of maps preserving matrix invariants; in particular, as an intermediate step, we characterize pairs of surjective maps φ1,φ2:Mn→Mn such that A+B is singular if and only if φ1(A)+φ2(B) is singular.",

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T1 - Automorphisms of the total digraph for the ring of square matrices over a field

AU - Costara, C.

AU - Guterman, A. E.

AU - Maksaev, A. M.

AU - Promyslov, V. V.

PY - 2023/6/1

Y1 - 2023/6/1

N2 - In this paper, we characterize the automorphisms of the total graph for the ring Mn of matrices of order n≥2 over any field with at least 3 elements. To do this, we apply the technique of maps preserving matrix invariants; in particular, as an intermediate step, we characterize pairs of surjective maps φ1,φ2:Mn→Mn such that A+B is singular if and only if φ1(A)+φ2(B) is singular.

AB - In this paper, we characterize the automorphisms of the total graph for the ring Mn of matrices of order n≥2 over any field with at least 3 elements. To do this, we apply the technique of maps preserving matrix invariants; in particular, as an intermediate step, we characterize pairs of surjective maps φ1,φ2:Mn→Mn such that A+B is singular if and only if φ1(A)+φ2(B) is singular.

KW - Automorphisms of graphs

KW - Determinant

KW - Nonlinear preserver

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U2 - 10.1016/j.laa.2023.03.007

DO - 10.1016/j.laa.2023.03.007

M3 - مقالة

SN - 0024-3795

VL - 666

SP - 129

EP - 143

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Automorphisms of the total digraph for the ring of square matrices over a field

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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