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Typical ranks of certain 3-tensors and absolutely full column rank tensors

By Mitsuhiro Miyazaki, Toshio Sumi and Toshio Sakata

Abstract

In this paper, we study typical ranks of 3-tensors and show that there are plural typical ranks for m\times n\times p tensors over R in the following cases: (1) 3\leq m\leq \rho(n) and (m-1)(n-1)+1\leq p\leq (m-1)n, where \rho\ is the Hurwitz-Radon function, (2) m=3, n\equiv 3\pmod 4 and p=2n-1, (3) m=4, n\equiv 2\pmod 4, n\geq 6 and p=3n-2, (4) m=6, n\equiv 4\pmod 8, n\geq 12 and p=5n-4. (5) m=10, n\equiv 24\pmod{32} and p=9n-8

Topics: Mathematics - Rings and Algebras, Mathematics - Statistics Theory, 15A69, 15A15, 65F40, 14E05, 11R52, 15A03, 65F05, 12D15, 14Q99, 14P05, 14M12
Year: 2012
OAI identifier: oai:arXiv.org:1103.0154
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