... theorem1
In modern form, much generalized, this is the famous Kodaira-Hodge-De Rham decomposition theorem[6] 
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... body.2
A beautiful treatment of this topic, as well as of the whole vector analysis, is found in Sommerfeld's Mechanics of Deformable Bodies.[5] 
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... deformation.3
This is, in fact, the decomposition, following Weyl[3], of the tensor $T_{li}$ into its irreducible components under rotations. This corresponds to analysing an infinitesimal deformation in terms of quantities which transform as irreducible representations of the rotation group. In particular, the traceless symmetric tensor ``carries'' an irreducible representation of dimension 5, an anisotropic object. 
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