Rank of n-tensors with size 2 ×...× 2

Toshio Sumi, Toshio Sakata, Mitsuhiro Miyazaki

研究成果: Contribution to journalArticle査読

抄録

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.

本文言語英語
ページ(範囲)141-162
ページ数22
ジャーナルFar East Journal of Mathematical Sciences
90
2
出版ステータス出版済み - 7 2014

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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