Rank decomposition and symmetric rank decomposition over arbitrary fields

2021/05/31 by Riguang Huang, Baodong Zheng, Xiaoyu Song · 6 citations
Chemistry · Engineering · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Chemistry #Combinatorics #Conjecture #Decomposition #Elementary symmetric polynomial #Exact solutions in general relativity #Mathematical analysis #Mathematics #Order (exchange) #Pure mathematics #Rank (graph theory) #Ring of symmetric functions #Sparse and Compressive Sensing Techniques #Symmetric closure #Symmetric tensor #Tensor (intrinsic definition) #Tensor decomposition and applications

paper · doi:10.1080/03081087.2021.1935436

published in Linear and Multilinear Algebra 70(20), 5888-5901 (Taylor & Francis)

openalex publication_date 2021/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Abstract

We give a necessary and sufficient condition for symmetric tensors to have symmetric rank decompositions and give some further results on the Comon's Conjecture (i.e. the rank and symmetric rank agree for a symmetric tensor). In particular, as an application, we prove that if an m-order 2-dimensional symmetric tensor has a symmetric rank decomposition, then its symmetric rank equals its rank or its rank plus one.

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