Xiong Zhu-hua, Zheng Quan-shui. Canonical Representations and Degree of Freedom Formulae of Orthogonal Tensors in n-Dimensional Euclidean Space[J]. Applied Mathematics and Mechanics, 1989, 10(1): 85-93.
Citation: Xiong Zhu-hua, Zheng Quan-shui. Canonical Representations and Degree of Freedom Formulae of Orthogonal Tensors in n-Dimensional Euclidean Space[J]. Applied Mathematics and Mechanics, 1989, 10(1): 85-93.

Canonical Representations and Degree of Freedom Formulae of Orthogonal Tensors in n-Dimensional Euclidean Space

  • Received Date: 1987-07-11
  • Publish Date: 1989-01-15
  • 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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