The maximum rank of 2 x MIDLINE HORIZONTAL ELLIPSIS x 2 tensors over F&xdd3d;2

被引：0
|
作者：
Stavrou, Stavros Georgios [1 ]
Low, Richard M. [2 ]
机构：
[1] Univ Saskatchewan, Dept Math & Stat, Saskatoon, SK, Canada
[2] San Jose State Univ, Dept Math & Stat, San Jose, CA 95192 USA
来源：
LINEAR & MULTILINEAR ALGEBRA | 2021年 / 69卷 / 03期
关键词：
Multidimensional arrays; tensor rank; finite fields; computer algebra; CLASSIFICATION; ARRAYS;
D O I：
10.1080/03081087.2020.1758019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We determine that the maximum rank of an order-n (>= 2) tensor with form at 2 x .... x 2 over the finite field F-2 is 2 . 3(n/2-1) for even n, and 3([n/2]) for odd n. Since tensor rank is non-increasing upon taking field extensions, F-2 gives the largest rank attainable for this tensor format. We also determine a maximum rank canonical form and compute its orbit under the action of the symmetry group GL(2)(F-2)(xn), and prove that this is the unique maximum rank canonical form, for even n >= 2.
引用
收藏
页码：394 / 402
页数：9
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