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arXiv · 1306.0708

Rank of tensors with size 2 x ... x 2

Toshio Sumi·Toshio Sakata·Mitsuhiro Miyazaki
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Abstract

We study an upper bound of ranks of $n$-tensors with size $2\times\cdots\times2$ over the complex and real number field. We characterize a $2\times 2\times 2$ 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 $2\times2\times2\times2$ complex tensors is 4. We state supporting evidence of the claim that 5 is a typical rank of $2\times2\times2\times2$ real tensors. Recall that Kong and Jiang show that the maximal rank of $2\times2\times2\times2$ real tensors is less than or equal to 5. The maximal rank of $2\times2\times2\times2$ complex (resp. real) tensors gives an upper bound of the maximal rank of $2\times\cdots\times 2$ complex (resp. real) tensors.

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Toshio Sumi, Toshio Sakata, Mitsuhiro Miyazaki. 2013-06-04. Rank of tensors with size 2 x ... x 2. https://arxiv.org/abs/1306.0708

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