Tensor ranks and symmetric tensor ranks are the same for points with low symmetric tensor rank

被引：0

作者：

Ballico, E. ^{[1
]}

机构：

[1] Univ Trent, Dept Math, I-38123 Povo, TN, Italy

来源：

ARCHIV DER MATHEMATIK | 2011年 / 96卷 / 06期

关键词：

Tensor rank; Symmetric tensor rank; Segre variety; Veronese variety;

D O I：

10.1007/s00013-011-0274-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Fix integers n >= 1, d >= 2. Let V be an (n + 1)-dimensional vector space over a field with characteristic zero. Fix a symmetric tensor T is an element of S(d)(V) subset of V(circle times d). Here we prove that the tensor rank of T is equal to its symmetric tensor rank if the latter is at most (d + 1)/2.

引用

页码：531 / 534

页数：4

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