Canonical representations and degree of freedom formulae of orthogonal tensors in n-dimensional Euclidean space |
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Authors: | Xiong Zhu-hua Zheng Quan-shui |
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Affiliation: | 1. Hunan University, Changsha;2. Jiangxi Polytechnic University, Nanchang |
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Abstract: | In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part of n/2. Finally, the formulae of the degree of freedom of orthogonal tensors are given. |
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