E-CHARACTERISTIC POLYNOMIALS OF TENSORS

被引：0

作者：

Li, An-Min ^{[1
]}

Qi, Liqun ^{[2
]}

Zhang, Bin ^{[1
]}

机构：

[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2013年 / 11卷 / 01期

关键词：

E-eigenvalues; tensors; E-characteristic polynomials; eigenpair equivalence class; irregularity; EIGENVALUES; RANK;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we show that the coefficients of the E-characteristic polynomial of a tensor are orthonormal invariants of that tensor. When the dimension is 2, some simplified formulas of the E-characteristic polynomial are presented. A resultant formula for the constant term of the E-characteristic polynomial is given. We prove that both the set of tensors with infinitely many eigenpairs and the set of irregular tensors have codimension 2 as subvarieties in the projective space of tensors. This makes our perturbation method workable. By using the perturbation method and exploring the difference between E-eigenvalues and eigenpair equivalence classes, we present a simple formula for the coefficient of the leading term of the E-characteristic polynomial when the dimension is 2.

引用

页码：33 / 53

页数：21

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