Representing Tensor Functions with a Cholesky Transform

The tensor representation theorem provides a powerful tool for evaluating isotropic tensor-valued tensor functions. Efficient computational techniques exist when an analysis is being done in rectangular Cartesian coordinates. Introducing a Cholesky decomposition of the metric tensor permits the tensor polynomial of the tensor representation theorem, when expressed in curvilinear coordinates, to be transformed into a pseudo-Cartesian frame where these efficient algorithms apply. It also leads to accurate descriptions for the physical components of a tensor.