线性局部B-保控映射的刻画  

Characterization of Local Preserving B-Majorization Linear Mapping

作　　者：刘菲 朱军[1] LIU Fei;ZHU Jun(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院

出　　处：《杭州电子科技大学学报（自然科学版）》2019年第6期84-87,共4页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(11801123)

摘　　要：设A,B∈M n×m。如果存在一个广义泛双随机矩阵D,使得A=DB,称A受B的B-控制,记作A B B。线性映射φ:M n×m→M n×m,如果对任意X∈M n×m,存在一个依赖于X的线性映射φX,使得φ(X)=φX(X),则称作局部B-保控映射。文中证明了对任意X∈M n×m,当n≥3时,线性映射φ是局部B-保控映射,当且仅当φ是B-保控映射。Let A,B∈M n×m.A is said to be of B-majorization of B,if there exist a generalized substochastic matrix D,such that A=DB and write A B B.Letφ:M n×m→M n×m be a linear mapping.φis said to be of local preserving B-majorization if,for each X∈M n×m,there exist a linear mappingφX of preserving B-majorization,which is depended on X,such thatφ(X)=φX(X).In this paper,we prove that for each X∈M n×m,φis a local preserving B-majorization if and only ifφis a preserving B-majorization when n≥3.

关 键 词：n×m的矩阵空间 局部B-保控 符号置换矩阵 

分 类 号：O151.2[理学—数学]