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.
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