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# Communications in Mathematical Sciences

## Volume 11 (2013)

### Number 1

### E-characteristic polynomials of tensors

Pages: 33 – 53

DOI: http://dx.doi.org/10.4310/CMS.2013.v11.n1.a2

#### Authors

#### Abstract

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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

65H17