矩阵空间上秩加性的加法保持(英文)  

Additive preservers of rank-additivity on matrix spaces

作　　者：Wai-Leong Chooi Ming-Huat Lim 

机构地区：[1]Multimedia大学工程系,Selangor,Cyberjaya 63100,马来西亚 [2]Malaya大学数学科学学院,Kuala Lumpur 50603,马来西亚

出　　处：《黑龙江大学自然科学学报》2004年第4期46-49,共4页Journal of Natural Science of Heilongjiang University

基　　金：Supported in part by an IRPA research grant from the Ministry of Science; Technology and Innovation ofMalaysia

摘　　要：设F是域,V是或者域F上所有m × n矩阵的空间或者是特征不为2及3的域F上所有n × n对称矩阵的空间.对于每个被固定的正整数s ≥ 2,Qs定义V × V中满足rank(A + B) = rank(A) +rank(B) ≤ s的所有矩阵对(A,B)的集合.刻划了V上满足Ψ(Qs) ? Qs的加法映射Ψ.当charF =2时,也描述了F上从n × n矩阵空间到p × q矩阵空间保秩加性的线性算子的结构.Let F be a ?eld. Let V denote the vector space of all m × n matrices over F or the vector space of all n × n symmetric matrices over F of characteristic not 2 or 3. For each ?xed positive s>2, let Qs denote the set of all matrix pairs (A,B) in V such that rank(A + B) = rank(A) + rank(B) 6 s. The authors characterize additive mappings ψ on V × V such that ψ(Qs) ? Qs for a ?xed s. They also describe the structure of linear mappings from the space of n × n matrices over Fto space of p × q matrices over F that preserve rank-additivity, where char = 2. F

关 键 词：加法映射 秩可加性 张量空间 对称空间 

分 类 号：O151.21[理学—数学]