2013/06/04 by Sumi, Toshio, Sakata, Toshio, Miyazaki, Mitsuhiro
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1306.0708
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 show 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.