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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

Postal Subscription Code 80-964

2018 Impact Factor: 0.565

Front. Math. China    2019, Vol. 14 Issue (1) : 225-237    https://doi.org/10.1007/s11464-019-0741-4
RESEARCH ARTICLE
Characteristic polynomial and higher order traces of third order three dimensional tensors
Guimei ZHANG1, Shenglong HU2,1()
1. School of Mathematics, Tianjin University, Tianjin 300350, China
2. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
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Abstract

Eigenvalues of tensors play an increasingly important role in many aspects of applied mathematics. The characteristic polynomial provides one of a very few ways that shed lights on intrinsic understanding of the eigenvalues. It is known that the characteristic polynomial of a third order three dimensional tensor has a stunning expression with more than 20000 terms, thus prohibits an effective analysis. In this article, we are trying to make a concise representation of this characteristic polynomial in terms of certain basic determinants. With this, we can successfully write out explicitly the characteristic polynomial of a third order three dimensional tensor in a reasonable length. An immediate benefit is that we can compute out the third and fourth order traces of a third order three dimensional tensor symbolically, which is impossible in the literature.

Keywords Tensor      traces      characteristic polynomial     
Corresponding Author(s): Shenglong HU   
Issue Date: 22 March 2019
 Cite this article:   
Guimei ZHANG,Shenglong HU. Characteristic polynomial and higher order traces of third order three dimensional tensors[J]. Front. Math. China, 2019, 14(1): 225-237.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0741-4
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I1/225
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