# Typical ranks of semi-tall real 3-tensors

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

## 抄録

Let m, n and p be integers with (Formula presented.) and (Formula presented.). We showed in previous papers that if (Formula presented.), then typical ranks of (Formula presented.) -tensors over the real number field are p and p+1 if and only if there exists a non-singular bilinear map (Formula presented.). We also showed that the ‘if’ part is also valid in the case where (Formula presented.). In this paper, we consider the case where (Formula presented.) and show that the typical ranks of (Formula presented.) -tensors over the real number field are p and p+1 in several cases including the case where there is no non-singular bilinear map (Formula presented.). In particular, we show that the ‘only if’ part of the above mentioned fact is not valid for the case (Formula presented.).

本文言語 英語 1734-1746 13 Linear and Multilinear Algebra 69 9 https://doi.org/10.1080/03081087.2019.1637811 出版済み - 2021

• 代数と数論

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