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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Communicated by Yang Gui-tong
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Zhu-hua, X., Quan-shui, Z. Canonical representations and degree of freedom formulae of orthogonal tensors in n-dimensional Euclidean space. Appl Math Mech 10, 93–101 (1989). https://doi.org/10.1007/BF02018496
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DOI: https://doi.org/10.1007/BF02018496