Typical ranks of certain 3-tensors and absolutely full column rank tensors

2011/03/01 by Mitsuhiro Miyazaki, Miyazaki, Mitsuhiro, Toshio Sumi +3
Mathematics · #11R52 #12D15 #14E05 #14M12 #14P05 #14Q99 #15A03 #15A15 #15A69 #65F05 #65F40 #FOS: Mathematics #Rings and Algebras (math.RA) #Statistics Theory (math.ST) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1103.0154

openalex publication_date 2011/03/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we study typical ranks of 3-tensors and show that there are plural typical ranks for m× n× p tensors over R in the following cases: (1) 3≤ m≤ ρ(n) and (m-1)(n-1)+1≤ p≤ (m-1)n, where ρ is the Hurwitz-Radon function, (2) m=3, n≡ 3\pmod 4 and p=2n-1, (3) m=4, n≡ 2\pmod 4, n≥ 6 and p=3n-2, (4) m=6, n≡ 4\pmod 8, n≥ 12 and p=5n-4. (5) m=10, n≡ 24\pmod32 and p=9n-8.

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