The tensor product is not a beast. If you know Einstein sum convention, you know the tensor product. With tensors written out explicitly with indices, it is qui

The tensor product is not a beast. If you know Einstein sum convention, you know the tensor product. With tensors written out explicitly with indices, it is quite easy to follow. The only thing you need to differentiate (and not even need to understand in order to perform calculations) are co/contravariant indices, aka "upper" and "lower" indices. Then it is just A_{ijk}^{abc} B_{ab}^{i} = C_c^{jk} and you are done. Read primers about general relativity if you want to get warm with the concept from an applied point of view (i.e. not mathematical one, but one where one wants to compute something).