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I am working through a textbook on general relativity and have come across the statement:

"A general (2 0) tensor K, in n dimensions, cannot be written as a direct product of two vectors, A and B, but can be expressed as a sum of many direct products."

Can someone explain to me how this is the case? Am I right in thinking that a (2 0) tensor is the tensor product of two vectors, so how then is the direct product of two vectors different to the tensor product?

Thanks!

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# Direct Product vs Tensor Product

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