About the maximal rank of 3-tensors over the real and the complex number field

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

研究成果: Contribution to journalArticle査読

4 被引用数 (Scopus)

抄録

Tensor data are becoming important recently in various application fields. In this paper, we consider themaximal rank problem of 3-tensors and extend Atkinson and Stephens' and Atkinson and Lloyd's results over the real number field. We also prove the assertion of Atkinson and Stephens: max.rankR(m, n, p) ≤ m + [p/2]n, max.rankR(n, n, p) ≤ (p+1)n/2 if p is even, max.rankF(n, n, 3) ≤ 2n-1 if F = C or n is odd, and max.rankF(m, n, 3) ≤ m +n-1 if m < n where F stands for ℝ or ℂ .

本文言語英語
ページ(範囲)807-822
ページ数16
ジャーナルAnnals of the Institute of Statistical Mathematics
62
4
DOI
出版ステータス出版済み - 8 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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