The E-characteristic polynomial of a tensor of dimension 2

Shenglong Hu, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

We show that the E-characteristic polynomial ψτ(λ ) of a tensor T of order m<3 and dimension 2 is ψτ(λ)=det(S-λT) with S a variant of the Sylvester matrix of the system Txm-1=0, and T a constant matrix that is only dependent on m. By exploring special structures of the matrices S and T, the coefficients of the E-characteristic polynomial ψτ(λ) which make the computation of ψτ(λ) efficient are obtained. On the basis of these, we prove that the leading coefficient of ψτ(λ) is (pm2+qm2)m-2/2 when m is even and -( pm2+qm2)m-2when m is odd, which strengthens Li, Qi and Zhang's theorem.
Original languageEnglish
Pages (from-to)225-231
Number of pages7
JournalApplied Mathematics Letters
Volume26
Issue number2
DOIs
Publication statusPublished - 1 Feb 2013

Keywords

  • E-characteristic polynomial
  • E-eigenvalue
  • Tensor

ASJC Scopus subject areas

  • Applied Mathematics

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