Polar decomposition theorem

Since the deformation tensor F is nonsingular, it may be decomposed uniquely into a proper orthogonal tensor R and a positive-definite symmetric tensor U by the polar decomposition theorem... 

Another approach to the analysis of Jones and Mueller-Jones matrix exploits the polar decomposition theorem [18]. This approach was first suggested in [19] and was explored in [20,21]. The polar decomposition of a Jones matrix J can be represented as ... 

We can define other deformation tensors, also, in terms of the deformation gradient tensor F. According to the polar decomposition theorem of the second-order tensor (see Appendix 2A), the deformation gradient tensor F, which is an asymmetric tensor and is assumed to be nonsingular (i.e., det F 0), can be expressed as a product of a positive symmetric tensor with an orthogonal tensor (Jaunzemis 1967) ... 

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