
Tensor product vs. direct product vs. Cartesian product (2016) - adamnemecek
http://www.boris-belousov.net/2016/06/22/tensor-products/
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ktpsns
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).

