Some norm inequalities for commutators of contracted tensor products

被引：2

作者：

Xie, Ze-Jia ^{[1
]}

Cheng, Che-Man ^{[2
]}

Jin, Xiao-Qing ^{[2
]}

机构：

[1] Dongguan Univ Technol, Dept Math & Data Sci, Dongguan 523808, Peoples R China

[2] Univ Macau, Dept Math, Macau, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 540卷

关键词：

Contracted product; Matricization; Tensor; Norm inequality; Commutator; WENZELS CONJECTURE; FROBENIUS NORM; MATRICES; BOTTCHER; PROOF;

D O I：

10.1016/j.laa.2017.11.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper concerns generalizations of the Bottcher Wenzel inequality to contracted products of tensors. We show that the best constant in the inequality is as expected in some cases and present an example where the best constant is larger than expected. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：244 / 256

页数：13

共 20 条

[1]

[Anonymous], 2013, MATRIX COMPUTATIONS

[2] Variance bounds, with an application to norm bounds for commutators [J].

Audenaert, Koenraad M. R. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (05) :1126-1143

[3] Algorithm 862: MATLAB tensor classes for fast algorithm prototyping [J].

Bader, Brett W. ;

Kolda, Tamara G. .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2006, 32 (04) :635-653

[4] The Frobenius norm and the commutator [J].

Boettcher, Albrecht ;

Wenzel, David .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (8-9) :1864-1885

[5] How big can the commutator of two matrices be and how big is it typically? [J].

Böttcher, A ;

Wenzel, D .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 403 :216-228

[6] Some sharp bounds for the commutator of real matrices [J].

Cheng, Che-Man ;

Liang, Yaru .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 521 :263-282

[7] A SURVEY ON THE BOTTCHER-WENZEL CONJECTURE AND RELATED PROBLEMS [J].

Cheng, Che-man ;

Jin, Xiao-qing ;

Vong, Seak-weng .

OPERATORS AND MATRICES, 2015, 9 (03) :659-673

[8] On Schatten p-norms of commutators [J].

Cheng, Che-Man ;

Lei, Chunyu .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 484 :409-434

[9] Commutators with maximal Frobenius norm [J].

Cheng, Che-Man ;

Vong, Seak-Weng ;

Wenzel, David .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (01) :292-306

[10]

Cichocki A., 2016, ARXIV160900893V1

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