Communications in Mathematical Sciences

Volume 11 (2013)

Number 1

E-characteristic polynomials of tensors

Pages: 33 – 53



An-Min Li (School of Mathematics, Sichuan University, Chengdu, China)

Liqun Qi (Department of Applied Mathematics, The Hong Kong Polytechnic University)

Bin Zhang (School of Mathematics, Sichuan University, Chengdu, China)


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.


E-eigenvalues, tensors, E-characteristic polynomials, eigenpair equivalence class, irregularity

2010 Mathematics Subject Classification


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