Communications in Mathematical Sciences
Volume 11 (2013)
E-characteristic polynomials of tensors
Pages: 33 – 53
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