On the tensor rank of 3× 3 permanent and determinant

01/01/2018

∙

by   Siddharth Krishna, et al.

∙

0

∙

share

The tensor rank and border rank of the 3 × 3 determinant tensor is known to be 5 if characteristic is not two. In this paper, we show that the tensor rank remains 5 for fields of characteristic two as well. We also include an analysis of 5 × 5 and 7 × 7 determinant and permanent tensors, as well as the symmetric 3 × 3 permanent and determinant tensors. We end with some remarks on binary tensors.