Typical ranks of semi-tall real 3-tensors

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

研究成果: Contribution to journalArticle査読

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
ページ(範囲)1734-1746
ページ数13
ジャーナルLinear and Multilinear Algebra
69
9
DOI
出版ステータス出版済み - 2021

All Science Journal Classification (ASJC) codes

  • 代数と数論

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