An equivalent condition for linear preservers of multivariate group majorization on matrices

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

2 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

10.22072/wala.2023.2006793.1428

Abstract

T. Ando characterized linear preservers of majorization in  [Linear Algebra Appl. 118 (1989) 163-248]. In this note, we present a method to state a simple proof of Ando's theorem. By using this method, we state an equivalent condition for matrix representations of linear preservers of $G$-majorization on matrices, where  $G$ is a finite subgroup of orthogonal  group $O(\mathbb{R}^n)$.
Moreover, we introduce reflective majorization and characterize all its linear preservers.

Keywords

References

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Wavelet and Linear Algebra
Volume 10, Issue 2
Autumn- Winter
2023
Pages 71-80

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