Deconvolution of tensors

Any second-rank tensor, T, can be decomposed into the sum of a symmetric, S, and an antisymmetric, A, tensor, i.e. in matrix notation 

Evidently, the antisymmetric tensor is traceless. The symmetric tensor can be made traceless by subtracting one-third of the trace 

Nine components of the tensor T have been transformed into three independent components of A (i.e. Ayz, Azx, Axy), five independent components of So (i.e. Syz, Sxz, Sxy, Sxx, Syy Szz is a dependent component since 

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