R^n上的线性局部保控映射  

Linear Mappings of Local Preserving-majorization on R^n

作　　者：李盼[1] 朱军[1] 

机构地区：[1]杭州电子科技大学数学研究所,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2015年第3期89-92,共4页Journal of Hangzhou Dianzi University：Natural Sciences

摘　　要：设φ:Rn→Rn是一个线性映射,对任意x∈Rn,都存在与x有关的线性保控映射ψx,使得φ(x)=ψx(x),则称φ是欧氏空间上的一个线性局部保控映射。线性保控映射是线性局部保控映射,其逆命题不成立。文中定义了两个与φ相关的Rn的子集Iφ和IIφ,如果任意Rn上的点都属于Iφ(或IIφ),那么这个线性局部保控映射φ是线性保控映射。Let φ： R^n → R^nbe a linear mapping. φ is said to be a linear mapping of local preservingmajorization on Euclidean space if for each x in R^n,there exists a linear mapping of preserving-majorization ψx which is depended on x such that φ（ x） = ψx（ x）. In this paper,it shows that a linear mapping of preservingmajorization must be of local preserving-majorization and its contrary is not true. Define two subsets Iφand IIφof R^nthat are related to φ（ definition 4）,if all the points in R^nbelong to Iφ（ or IIφ）,then φ is a linear mapping of preserving-majorization.

关 键 词：欧氏空间 线性局部保控映射 线性保控映射 

分 类 号：O151.2[理学—数学]