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.

引用

页码：255 / 271

页数：17

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