Linear preservers ‎of acu-majorization on ‎‎‎\mathbb{R}^۳‎ and ‎‎M_{۳,m}‎‎‎‎

‎‎In this note, we present an equivalent condition for linear preservers of group majorization induced by closed subgroup G of O(\mathbb{R}^n). Moreover, a new concept of majorization  is defined on \mathbb{R}^۳ as acu-majorization and this is extended for ۳ \times m matrices. Then we characterize all its linear preservers on \mathbb{R}^۳ and M_{۳,m}.

Keywords:

Majorization , group majorization , circulant majorization , linear preservers