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

Toshio Sumi; Mitsuhiro Miyazaki; Toshio Sakata

doi:10.1080/03081087.2014.910206

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

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

Division for Theoretical Natural Science

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	940-955
Number of pages	16
Journal	Linear and Multilinear Algebra
Volume	63
Issue number	5
DOIs	https://doi.org/10.1080/03081087.2014.910206
Publication status	Published - May 4 2015

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1080/03081087.2014.910206

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

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.).",

author = "Toshio Sumi and Mitsuhiro Miyazaki and Toshio Sakata",

note = "Funding Information: This work was supported partially by JSPS KAKENHI [grant number 24540131]. Publisher Copyright: {\textcopyright} 2014, {\textcopyright} 2014 Taylor & Francis.",

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AU - Sumi, Toshio

AU - Miyazaki, Mitsuhiro

AU - Sakata, Toshio

PY - 2015/5/4

Y1 - 2015/5/4

N2 - 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.).

AB - 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.).

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ER -

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

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