An upper bound for the real tensor rank and the real symmetric tensor rank in terms of the complex ranks

被引：4

作者：

Ballico, E. ^{[1
]}

机构：

[1] Univ Trent, Dept Math, Povo, TN, Italy

来源：

LINEAR & MULTILINEAR ALGEBRA | 2014年 / 62卷 / 11期

关键词：

symmetric tensor rank; tensor rank; Segre variety; Veronese variety; real rank; finite field;

D O I：

10.1080/03081087.2013.839671

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Fix a real tensor T of format (m(1),..., m(s)). Here we prove that its real tensor rank is at most s times its complex tensor rank. A similar bound is true for symmetric tensors and for any perfect field (e.g. a finite field).

引用

页码：1546 / 1552

页数：7

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