Hey it might be a stupid question but I saw that the tensor product of 2 vectors with dim m and n gives another vector with dimension mn and in another context I saw that the tensor product of vector gives a metrix. For example from sean carroll's book: "If T is a (k,l) tensor and S is a (m, n) tensor, we define a (k + m, l + n) tensor T ⊗ S"(adsbygoogle = window.adsbygoogle || []).push({});

so the tensor product of two type 1 tensors,k=1,vectors, is a metrix

and in the context of quantum mechanic I saw

(1,0)⊗(1,0)↦(1,0,0,0) when those our basis vectors.

I'm sure I'm just getting something wrong but I am hopefull that you can explain me what.

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# A question about tensor product

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