Typical ranks of m × n × (m − 1)n tensors with 3 ≤ m ≤ n over the real number field

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

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2 Citations (Scopus)

Abstract

Let (Formula presented.). We study typical ranks of (Formula presented.) tensors over the real number field. Let (Formula presented.) be the Hurwitz–Radon function defined as (Formula presented.) for nonnegative integers (Formula presented.) such that (Formula presented.) and (Formula presented.). If (Formula presented.), then the set of (Formula presented.) tensors has two typical ranks (Formula presented.). In this paper, we show that the converse is also true: if (Formula presented.), then the set of (Formula presented.) tensors has only one typical rank (Formula presented.).

Original languageEnglish
Pages (from-to)940-955
Number of pages16
JournalLinear and Multilinear Algebra
Volume63
Issue number5
DOIs
Publication statusPublished - May 4 2015

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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