Question: Show that an arbitrary tensor A can be expressed as the sum of a spherical tensor (i.e., a scalar multiple of the identity tensor)

Show that an arbitrary tensor A can be expressed as the sum of a spherical tensor (i.e., a scalar multiple of the identity tensor) and a tensor with zero trace. Prove that this decomposition is unique and that A', the traceless part of A, is given by where A' is the deviator of A. 1 A'= A--(tr A) I 3

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