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

Author(s):

Mohammad Soleymani * , Abbas Salemi

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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:

Majorization , Group majorization , Linear preservers , Doubly stochastic matrices , Permutation

Language:
English
Published:
Wavelets and Linear Algebra, Volume:10 Issue: 2, Autumn and Winter 2023
Pages:
71 to 80
https://www.magiran.com/p2680358