publication . Preprint . 2017

Transposes, L-Eigenvalues and Invariants of Third Order Tensors

Qi, Liqun;
Open Access English
  • Published: 05 Apr 2017
Abstract
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order tensor into a first order tensor, or a first order tensor into a second order tensor. For a third order tensor, we define its transpose, kernel tensor and L-eigenvalues. Here...
Subjects
arXiv: Computer Science::Graphics
free text keywords: Mathematical Physics
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