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
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
收藏
页码:33 / 53
页数:21
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