Multivariate group majorization on M_n and its linear preservers |
کد مقاله : 1034-SLAA10 |
نویسندگان |
محمد سلیمانی باغشاه * گروه ریاضی، دانشکده ریاضی و کامپیوتر، دانشگاه شهید باهنر کرمان،کرمان،ایران |
چکیده مقاله |
For $X,Y in M_{n,m}$, $X$ is said to be multivariate majorized by $Y$, denoted by $Xprec_m Y$, if there exists doubly stochastic matrix $D in M_n$ such that $X=DY$. In this paper, we extend multivariate majorization as a group majorization on $M_{n,m}$. Let $G$ be a subgroup of orthogonal group $O(mathbb{R}^n)$. We say that $X$ is $GM$-majorized by $Y$ (written as $X prec_{GM}Y$), if $X=sum_{i=1}^k c_ig_iY$ where $g_i in G$, $c_i geq 0$, $sum_{i=1}^k c_i=1$. We state equivalent conditions for linear preservers of multivariate group majorization. |
کلیدواژه ها |
matrix majorization, group majorization, linear preserver |
وضعیت: پذیرفته شده مشروط برای ارائه شفاهی |