Open AccessOn the tensor rank of the 3 x 3 permanent and determinant
Author(s) -
Siddharth Krishna,
Visu Makam
Publication year - 2021
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2021.5107
Subject(s) - rank (graph theory) , mathematics , tensor (intrinsic definition) , symmetric tensor , pure mathematics , mathematical proof , combinatorics , algebra over a field , mathematical analysis , geometry , exact solutions in general relativity
The tensor rank and border rank of the $3 \times 3$ determinant tensor are known to be $5$ if the characteristic is not two. In characteristic two, the existing proofs of both the upper and lower bounds fail. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well.