An Improvement on Ranks of Explicit Tensors
2011
We give constructions of n^k x n^k x n tensors of rank at least 2n^k - O(n^(k-1)). As a corollary we obtain an [n]^r shaped tensor with rank at least 2n^(r/2) - O(n^(r/2)-1) 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 previous best-known explicit tensors that had ranks n^k and n^(r/2) respectively
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
9
References
1
Citations
NaN
KQI