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

共 50 条

[31] Tensor Recovery With Weighted Tensor Average Rank
Zhang, Xiaoqin
Zheng, Jingjing
Zhao, Li
Zhou, Zhengyuan
Lin, Zhouchen
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2024, 35 (01) : 1142 - 1156
[32] Tensor rank is not multiplicative under the tensor product
Christandl, Matthias
Jensen, Asger Kjaerulff
Zuiddam, Jeroen
LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 543 : 125 - 139
[33] CONFORMALLY COVARIANT EQUATION OF SECOND RANK SYMMETRIC TENSOR FIELD
许伯威
A Monthly Journal of Science, 1984, (05) : 601 - 604
[34] On some bounds for symmetric tensor rank of multiplication in finite fields
Ballet, Stephane
Pieltant, Julia
Rambaud, Matthieu
Sijsling, Jeroen
ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, 2017, 686 : 93 - 121
[35] CONFORMALLY INVARIANT EQUATION FOR THE SYMMETRIC TENSOR OF RANK-2
LEONOVICH, AA
DOKLADY AKADEMII NAUK BELARUSI, 1984, 28 (11): : 995 - 997
[36] SYMMETRIC TENSOR RANK WITH A TANGENT VECTOR: A GENERIC UNIQUENESS THEOREM
Ballico, Edoardo
Bernardi, Alessandra
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (10) : 3377 - 3384
[37] REAL HYPERSURFACES OF A NONFLAT COMPLEX SPACE FORM IN TERMS OF THE RICCI TENSOR
Ki, U-Hang
Nagai, Setsuo
TSUKUBA JOURNAL OF MATHEMATICS, 2005, 29 (02) : 511 - 532
[38] On the typical rank of real polynomials (or symmetric tensors) with a fixed border rank
Ballico E.
Acta Mathematica Vietnamica, 2014, 39 (3) : 367 - 378
[39] Real Hypersurfaces of Complex Quadric in Terms of Star-Ricci Tensor
Chen, Xiaomin
TOKYO JOURNAL OF MATHEMATICS, 2018, 41 (02) : 587 - 601
[40] The Optimization Landscape for Fitting a Rank-2 Tensor with a Rank-1 Tensor
Gong, Xue
Mohlenkamp, Martin J.
Young, Todd R.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2018, 17 (02): : 1432 - 1477

← 1 2 3 4 5 →