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.
Original language | English |
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Pages (from-to) | 33-53 |
Number of pages | 21 |
Journal | Communications in Mathematical Sciences |
Volume | 11 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2013 |
Keywords
- E-characteristic polynomials
- E-eigenvalues
- Eigenpair equivalence class
- Irregularity.
- Tensors
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics