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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.
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Keywords
Tensor
traces
characteristic polynomial
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Corresponding Author(s):
Shenglong HU
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Issue Date: 22 March 2019
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