### 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 language | English |
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Pages (from-to) | 193-205 |

Number of pages | 13 |

Journal | Linear and Multilinear Algebra |

Volume | 66 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2 2018 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Linear and Multilinear Algebra*,

*66*(1), 193-205. https://doi.org/10.1080/03081087.2017.1292994

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

Research output: Contribution to journal › Article

*Linear and Multilinear Algebra*, vol. 66, no. 1, pp. 193-205. https://doi.org/10.1080/03081087.2017.1292994

}

TY - JOUR

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

AU - Miyazaki, Mitsuhiro

AU - Sumi, Toshio

AU - Sakata, Toshio

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.

UR - http://www.scopus.com/inward/record.url?scp=85014457854&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014457854&partnerID=8YFLogxK

U2 - 10.1080/03081087.2017.1292994

DO - 10.1080/03081087.2017.1292994

M3 - Article

AN - SCOPUS:85014457854

VL - 66

SP - 193

EP - 205

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 1

ER -