We give constructions of n × n × n tensors of rank at least 2n − O(n). As a corollary we obtain an [n] shaped tensor with rank at least 2n − O(n) when r is odd. The tensors are constructed from a simple recursive pattern, and the lower bounds are proven using a partitioning theorem developed by Brockett and Dobkin. These two bounds are improvements over the… (More)

Ja’ and Jean Takche, On the Validity of the Direct Sum Conjecture

Joseph Ja

SIAM Journal on Computing Volume 15, Issue

1986

Ja’, Optimal Evaluation of Pairs of Bilinear Forms

Joseph Ja

SIAM Journal on Computing Volume 8, Issue

1979

On the Maximal Multiplicative Complexity of a Family of Bilinear Forms

M. D. Atkinson, N. M. Stephens

Linear Algebra and Its Applications Volume

1979

Three-Way Arrays: Rank and Uniqueness of Trilinear Decompositions, with Application to Arithmetic Complexity and Statistics, Linear Algebra and Its Applications