COMON'S CONJECTURE, RANK DECOMPOSITION, AND SYMMETRIC RANK DECOMPOSITION OF SYMMETRIC TENSORS

被引：21

作者：

Zhang, Xinzhen ^{[1
]}

Huang, Zheng-Hai ^{[1
]}

Qi, Liqun ^{[2
]}

机构：

[1] Tianjin Univ, Sch Sci, Dept Math, Tianjin 300072, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2016年 / 37卷 / 04期

基金：

中国国家自然科学基金;

关键词：

tensor; rank; symmetric rank; rank decomposition; symmetric rank decomposition;

D O I：

10.1137/141001470

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Comon's Conjecture claims that for a symmetric tensor, its rank and its symmetric rank coincide. We show that this conjecture is true under an additional assumption that the rank of that tensor is not larger than its order. Moreover, if its rank is less than its order, then all rank decompositions are necessarily symmetric rank decompositions.

引用

页码：1719 / 1728

页数：10

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