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

Qufu Normal University, Küfow, Shandong Sheng, China
(Impact Factor: 1.12). 05/2007; 329(2):1218-1229. DOI: 10.1016/j.jmaa.2006.07.064

ABSTRACT 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. (c) 2006 Elsevier Inc. All rights reserved.

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