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

Mitsuhiro Miyazaki, Toshio Sumi, Toshio Sakata

Research output: Contribution to journalArticle

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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 (mod 4) and p = 2n - 1, (3) m = 4, n ≡ 2 (mod 4), n ≥ 6 and p = 3n - 2, (4) m = 6, n ≥ 4 (mod 8), n ≡ 12 and p = 5n - 4. (5) m = 10, n ≥ 24 (mod 32) and p = 9n - 8.

Original languageEnglish
Pages (from-to)193-205
Number of pages13
JournalLinear and Multilinear Algebra
Volume66
Issue number1
DOIs
Publication statusPublished - Jan 2 2018

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Typical ranks of certain 3-tensors and absolutely full column rank tensors. / Miyazaki, Mitsuhiro; Sumi, Toshio; Sakata, Toshio.

In: Linear and Multilinear Algebra, Vol. 66, No. 1, 02.01.2018, p. 193-205.

Research output: Contribution to journalArticle

Miyazaki, Mitsuhiro ; Sumi, Toshio ; Sakata, Toshio. / Typical ranks of certain 3-tensors and absolutely full column rank tensors. In: Linear and Multilinear Algebra. 2018 ; Vol. 66, No. 1. pp. 193-205.
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