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

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

Research output: Contribution to journalArticle

3 Citations (Scopus)


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 .

Original languageEnglish
Pages (from-to)807-822
Number of pages16
JournalAnnals of the Institute of Statistical Mathematics
Issue number4
Publication statusPublished - Aug 1 2010


All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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