I am trying to show that if (C^ab)(A_a)(B_b) is a scalar for arbitrary vectors A_a and B_b then C^ab is a tensor.(adsbygoogle = window.adsbygoogle || []).push({});

I want to take the product of the two vectors then use the quotient rule to show that C^ab must then be a tensor. This lead to the question of whether or a not the product of two arbitrary vectors is again a completely arbitrary tensor. I guess this boils down to asking whether or not every tensor can be generated by a tensor product of two vectors.

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# Tensor product of two arbitrary vectors an arbitrary tensor?

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