E-Characteristic Polynomials of Tensors
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 re- sultant formula for the constant term of the E-characteristic polynomial is given. We then study the set of tensors with infinitely many eigenpairs and the set of irregular tensors, and prove both the sets 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.
Cite
@article{arxiv.1208.1607,
title = {E-Characteristic Polynomials of Tensors},
author = {An-Min Li and Liqun Qi and Bin Zhang},
journal= {arXiv preprint arXiv:1208.1607},
year = {2012}
}