(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The SR&GR guy aren't being very helpful, so maybe I can get this quickly resolved here.

I want to know if the product of two tensor fields is generally non-commutative. That is, if I have two tensor fields [itex] A_{ij}, B_k^\ell [/itex] do these representations commute?

3. The attempt at a solution

I feel generally quite conflicted about this subject, and I think it's because I don't fully understand what the representations mean. On one hand, I want to say that for a fixed i,j these simply represent scalar elements and so certainly commute. However, taken as general tensors (for example matrices), they would not commute. That is, if A and B were matrices, then [itex] AB \neq BA[/itex] in general, but given the representations [itex] (A)_{ij} = a_{ij}, (B)_{ij} = b_{ij} [/itex] then certainly [itex] a_{ij}b_{k\ell} = b_{k\ell} a_{ij} [/itex] - the only "non-commutativity" comes in the ordering of the indices. Can anybody shed some light on this situation?

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# Tensor Field Commutativity

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