I'm trying to prove what is shown in figure 1 where V is a vector and T is a tensor. However if I arbitrarily assign values to the vectors and tensors and try to prove it by performing the operation, I end up calculating that all three terms are exactly the same which obviously cannot be. Input anyone?
As I understand it, the dot product of a vector and a tensor is a vector so you could take the divergence of what is shown in the parenthesis.
Hmmmm.... I see what you are saying for a higher dimensional case, and I'll admit that I didn't think it through, but vectors with the correct transformation properties are tensors also and you can't do the problem when T is a vector.
Originally Posted by Jensen
Otherwise I think you can make the same argument that I did, just in a slightly different form. Now the are a set of vectors is the only difference.