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

Department of Mathematics, National University of Defense Technology, Changsha, Hunan 410073, PR China; Department of Mathematics, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong; Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong; School of Operations Research and Management Sciences, Qufu Normal University, Rizhao, Shandong 276800, PR China
Journal of Mathematical Analysis and Applications (Impact Factor: 1.12). 05/2007; 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.

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