Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/22826
Title: E-characteristic polynomials of tensors
Authors: Li, AM
Qi, L 
Zhang, B
Keywords: E-characteristic polynomials
E-eigenvalues
Eigenpair equivalence class
Irregularity.
Tensors
Issue Date: 2013
Source: Communications in mathematical sciences, 2013, v. 11, no. 1, p. 33-53 How to cite?
Journal: Communications in Mathematical Sciences 
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.
URI: http://hdl.handle.net/10397/22826
ISSN: 1539-6746
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