On the tensor rank of the 3 x 3 permanent and determinant

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2021-06-10 DOI:10.13001/ELA.2021.5107

Siddharth Krishna, V. Makam

引用次数: 2

Abstract

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.

查看原文本刊更多论文

关于3 × 3的恒量和行列式的张量秩

如果特征不为2，则已知$3 \乘以3$行列式张量的张量秩和边界秩为$5$。在特征二中，已有的上界和下界的证明都失败了。在本文中，我们证明了对于特征2的域，张量秩也保持$5$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.