The degree of the E-characteristic polynomial of an even order tensor

Guyan Ni, Liqun Qi, Fei Wang, Yiju Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

63 Citations (Scopus)


The E-characteristic polynomial of an even order supersymmetric tensor is a useful tool in determining the positive definiteness of an even degree multivariate form. In this paper, for an even order tensor, we first establish the formula of its E-characteristic polynomial by using the classical Macaulay formula of resultants, then give an upper bound for the degree of that E-characteristic polynomial. Examples illustrate that this bound is attainable in some low order and dimensional cases.
Original languageEnglish
Pages (from-to)1218-1229
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 May 2007


  • E-Characteristic polynomial
  • E-Eigenvalue
  • Resultant
  • Tensor
  • Upper bound

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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