Typical ranks of semi-tall real 3-tensors

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

Research output: Contribution to journalArticle

Abstract

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.).

Original languageEnglish
JournalLinear and Multilinear Algebra
DOIs
Publication statusPublished - Jan 1 2019

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Tensor
Bilinear Map
Number field
Valid
If and only if
Integer

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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Typical ranks of semi-tall real 3-tensors. / Sumi, Toshio; Miyazaki, Mitsuhiro; Sakata, Toshio.

In: Linear and Multilinear Algebra, 01.01.2019.

Research output: Contribution to journalArticle

Sumi, Toshio ; Miyazaki, Mitsuhiro ; Sakata, Toshio. / Typical ranks of semi-tall real 3-tensors. In: Linear and Multilinear Algebra. 2019.
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