### 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 language | English |
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Pages (from-to) | 141-162 |

Number of pages | 22 |

Journal | Far East Journal of Mathematical Sciences |

Volume | 90 |

Issue number | 2 |

Publication status | Published - Jul 2014 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Far East Journal of Mathematical Sciences*,

*90*(2), 141-162.