E-characteristic polynomials of tensors

An Min Li, Liqun Qi, Bin Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)

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 languageEnglish
Pages (from-to)33-53
Number of pages21
JournalCommunications in Mathematical Sciences
Volume11
Issue number1
DOIs
Publication statusPublished - 1 Jan 2013

Keywords

  • E-characteristic polynomials
  • E-eigenvalues
  • Eigenpair equivalence class
  • Irregularity.
  • Tensors

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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