Sets Computing the Symmetric Tensor Rank

被引：12

作者：

Ballico, Edoardo ^{[1
]}

Chiantini, Luca ^{[2
]}

机构：

[1] Univ Trento, Dipartimento Matemat, I-38123 Povo, TN, Italy

[2] Univ Siena, Dipartimento Sci Matemat & Informat R Magari, I-53100 Siena, Italy

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2013年 / 10卷 / 02期

关键词：

Symmetric tensor rank; Veronese embedding;

D O I：

10.1007/s00009-012-0214-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let denote the degree d Veronese embedding of . For any , the symmetric tensor rank sr(P) is the minimal cardinality of a set spanning P. Let be the set of all such that computes sr(P). Here we classify all such that sr(P) < 3d/2 and sr(P) is computed by at least two subsets of . For such tensors , we prove that has no isolated points.

引用

页码：643 / 654

页数：12

共 18 条

[11] On the Rank of a Binary Form
Comas, Gonzalo
Seiguer, Malena
[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2011, 11 (01) : 65 - 78
[12] SYMMETRIC TENSORS AND SYMMETRIC TENSOR RANK
Comon, Pierre
Golub, Gene
Lim, Lek-Heng
Mourrain, Bernard
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (03) : 1254 - 1279
[13] The dual minimum distance of arbitrary-dimensional algebraic-geometric codes
Couvreur, Alain
[J]. JOURNAL OF ALGEBRA, 2012, 350 (01) : 84 - 107
[14] TENSOR RANK AND THE ILL-POSEDNESS OF THE BEST LOW-RANK APPROXIMATION PROBLEM
de Silva, Vin
Lim, Lek-Heng
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (03) : 1084 - 1127
[15] Hartshorne R., 1977, Algebraic geometry, Graduate Texts in Mathematics, pxvi
[16] Tensor Decompositions and Applications
Kolda, Tamara G.
Bader, Brett W.
[J]. SIAM REVIEW, 2009, 51 (03) : 455 - 500
[17] On the Ranks and Border Ranks of Symmetric Tensors
Landsberg, J. M.
Teitler, Zach
[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2010, 10 (03) : 339 - 366
[18] Landsberg J. M., 2012, GRADUATE STUDIES MAT, V118

← 1 2 →