Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/31154
Title: The E-characteristic polynomial of a tensor of dimension 2
Authors: Hu, S
Qi, L 
Keywords: E-characteristic polynomial
E-eigenvalue
Tensor
Issue Date: 2013
Publisher: Pergamon Press
Source: Applied mathematics letters, 2013, v. 26, no. 2, p. 225-231 How to cite?
Journal: Applied mathematics letters 
Abstract: We show that the E-characteristic polynomial ψ τ(λ ) of a tensor T of order m<3 and dimension 2 is ψ τ(λ)=det(S-λT) with S a variant of the Sylvester matrix of the system Tx m-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 ψ τ(λ) which make the computation of ψ τ(λ) efficient are obtained. On the basis of these, we prove that the leading coefficient of ψ τ(λ) is (p m 2+q m 2)m-2/2 when m is even and -( p m 2+q m 2) m-2 when m is odd, which strengthens Li, Qi and Zhang's theorem.
URI: http://hdl.handle.net/10397/31154
ISSN: 0893-9659
DOI: 10.1016/j.aml.2012.08.017
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