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
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