Rank of n-tensors with size 2 ×...× 2

Toshio Sumi, Toshio Sakata, Mitsuhiro Miyazaki

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Abstract

We study an upper bound of ranks of n-tensors with size 2 ×... × 2 over the complex and real number field. We characterize a 2 × 2 × 2 tensor with rank 3 by using the Cayley's hyperdeterminant and some function. Then we see another proof of Brylinski's result that the maximal rank of 2 × 2 × 2 × 2 complex tensors is 4. We state supporting evidence of the claim that 5 is a typical rank of 2 × 2 × 2 × 2 real tensors. Recall that Kong and Jiang [9] showed that. the maximal rank of 2 × 2 × 2 × 2 real tensors is less than or equal to 5. The maximal rank of 2 × 2 × 2 × 2 complex (resp. real) tensors gives an upper bound of the maximal rank of 2 ×... × 2 complex (resp. real) tensors.

Original languageEnglish
Pages (from-to)141-162
Number of pages22
JournalFar East Journal of Mathematical Sciences
Volume90
Issue number2
Publication statusPublished - Jul 2014

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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