TY - JOUR

T1 - Typical ranks of m × n × (m − 1)n tensors with 3 ≤ m ≤ n over the real number field

AU - Sumi, Toshio

AU - Miyazaki, Mitsuhiro

AU - Sakata, Toshio

N1 - Funding Information:
This work was supported partially by JSPS KAKENHI [grant number 24540131].
Publisher Copyright:
© 2014, © 2014 Taylor & Francis.

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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U2 - 10.1080/03081087.2014.910206

DO - 10.1080/03081087.2014.910206

M3 - Article

AN - SCOPUS:84919860391

SN - 0308-1087

VL - 63

SP - 940

EP - 955

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 5

ER -