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Orthogonal irreducible decompositions of tensors of high orders. (English) Zbl 1028.74007

Summary: It is known from the theory of group representations that, in principle, a tensor of any finite order can be decomposed into a sum of irreducible tensors. This paper develops a simple and effective recursive method to realize such decompositions in both two- and three-dimensional spaces. Particularly, such derived decompositions have mutually orthogonal base elements. Quite a few application examples are given for generic and various physical tensors of orders up to six.

MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
15A72 Vector and tensor algebra, theory of invariants
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