Frontiers of Mathematics in China >
Characteristic polynomial and higher order traces of third order three dimensional tensors
Received date: 29 Mar 2018
Accepted date: 03 Dec 2018
Published date: 22 Mar 2019
Copyright
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.
Key words： Tensor; traces; characteristic polynomial
Guimei ZHANG , Shenglong HU . Characteristic polynomial and higher order traces of third order three dimensional tensors[J]. Frontiers of Mathematics in China, 2019 , 14(1) : 225 -237 . DOI: 10.1007/s11464-019-0741-4
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