Linear rank preservers of tensor products of rank one matrices

被引：6
|
作者：
Huang, Zejun [1 ]
Shi, Shiyu [2 ]
Sze, Nung-Sing [2 ]
机构：
[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
[2] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 508卷
关键词：
Linear preserver; Rank; Tensor product; Partial transpose; Realignment; SEPARABILITY CRITERION; ADDITIVE PRESERVERS;
D O I：
10.1016/j.laa.2016.07.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let n(1), ... ,n(k) be integers larger than or equal to 2. We characterize linear maps phi. : M-n1 ... nk -> M-n1 ... nk such that rank (phi(A1 circle times ... circle times A(k))) = 1 whenever rank (A1 circle times ... circle times A(k)) = 1 for all A(i) is an element of M-ni, i = 1, ..., k. Applying this result, we extend two recent results on linear maps that preserve the rank of special classes of matrices. (C) 2016 Elsevier Inc. All rights reserved.
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页码：255 / 271
页数：17
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