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

T. Ando characterized linear preservers of majorization in  [Linear Algebra Appl. ۱۱۸ (۱۹۸۹) ۱۶۳-۲۴۸]. 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:

مهتری , مهتری گروهی , نگهدارنده های خطی , ماتریس های تصادفی مضاعف , جایگشت ها