TY - JOUR

T1 - Typical ranks of certain 3-tensors and absolutely full column rank tensors

AU - Miyazaki, Mitsuhiro

AU - Sumi, Toshio

AU - Sakata, Toshio

N1 - Funding Information:
The authors are supported partially by JSPS KAKENHI [grant number 20340021].
Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2018/1/2

Y1 - 2018/1/2

N2 - 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.

AB - 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.

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U2 - 10.1080/03081087.2017.1292994

DO - 10.1080/03081087.2017.1292994

M3 - Article

AN - SCOPUS:85014457854

SN - 0308-1087

VL - 66

SP - 193

EP - 205

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 1

ER -