Comon's conjecture, rank decomposition, and symmetric rank decomposition of symmetric tensors

Xinzhen Zhang; Zheng Hai Huang; Liqun Qi

doi:10.1137/141001470

Comon's conjecture, rank decomposition, and symmetric rank decomposition of symmetric tensors

Xinzhen Zhang, Zheng Hai Huang, Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

21 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1719-1728
Number of pages	10
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	37
Issue number	4
DOIs	https://doi.org/10.1137/141001470
Publication status	Published - 1 Jan 2016

Keywords

Rank
Rank decomposition
Symmetric rank
Symmetric rank decomposition
Tensor

ASJC Scopus subject areas

Analysis

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10.1137/141001470

Cite this

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AB - 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.

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KW - Symmetric rank decomposition

KW - Tensor

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DO - 10.1137/141001470

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Comon's conjecture, rank decomposition, and symmetric rank decomposition of symmetric tensors

Abstract

Keywords

ASJC Scopus subject areas

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