On the ranks of the third secant variety of Segre–Veronese embeddings. Issue 3 (4th March 2019)

• Record Type: Journal Article
• Authors: Ballico, Edoardo; Bernardi, Alessandra
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 3(2019)
• Page Start: 583
• Page End: 597
• Publication Date: 2019-03-04
• Subjects: Partially symmetric tensor -- border rank -- tensor rank; 15A69; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1430117
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: We give an upper bound for the rank of the border rank 3 partially symmetric tensors. In the special case of border rank 3 tensorsT ∈ V 1 ⊗ ⋯ ⊗ V k (Segre case) we can show that all ranks among 3 andk - 1 arise and ifdim V i ≥ 3 for all i 's, then all the ranks between k and2 k - 1 arise.