Partially symmetric tensor rank: the description of the non-uniqueness case for low rank. Issue 3 (4th March 2018)

• Record Type: Journal Article
• Authors: Ballico, E.
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 3(2018)
• Page Start: 608
• Page End: 624
• Publication Date: 2018-03-04
• Subjects: Partially symmetric tensor -- Segre–Veronese variety -- tensor rank -- X-rank; 15A69 -- 14N05; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1310177
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : We study the partially symmetric tensors T with low rank whose rank is not achieved by a unique set when the rank has an upper bound like, where is the minimum of the entries of the multidegree of T . For the proof, we use the Hilbert function of finite subsets of a product of projective spaces with respect to a Segre–Veronese embedding.