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antarctic

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I am trying to learn the theory of elasticity from Landau's book and from the very beginning I've run into trouble. As I learned it, a (0,2) tensor T_ij obeys the transformation law T_hk=T(dx_i/dx_h)(dx_j/dx_k). But I do not see how a strain tensor can be transformed in such a manner (I'm getting two extra terms at the end that don't seem to add to 0). How can you justify it being called a tensor then? Or does the transformation work, and I'm just not seeing something?

Any help appreciated.