Rank one preservers between spaces of Boolean matrices

被引：2
|
作者：
Lim, Ming-Huat [1 ]
Tan, Sin-Chee [1 ]
机构：
[1] Univ Malaya, Inst Math Sci, Kuala Lumpur 50603, Malaysia
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 434卷 / 02期
关键词：
Rank one preserver; Boolean matrix; Boolean vector space; Tensor product; OPERATORS;
D O I：
10.1016/j.laa.2010.09.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we characterize (i) linear transformations from one space of Boolean matrices to another that send pairs of distinct rank one elements to pairs of distinct rank one elements and (ii) surjective mappings from one space of Boolean matrices to another that send rank one matrices to rank one matrices and preserve order relation in both directions. Both results are proved in a more general setting of tensor products of two Boolean vector spaces of arbitrary dimension. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：526 / 541
页数：16
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