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

Xinzhen Zhang, Zheng Hai Huang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


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 languageEnglish
Pages (from-to)1719-1728
Number of pages10
JournalSIAM Journal on Matrix Analysis and Applications
Issue number4
Publication statusPublished - 1 Jan 2016


  • Rank
  • Rank decomposition
  • Symmetric rank
  • Symmetric rank decomposition
  • Tensor

ASJC Scopus subject areas

  • Analysis

Cite this