Tensor product

  • Thread starter antonio85
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Why these two tensor products are isomorphic?

[tex]Hom_{K}(V,K) \otimes Hom_{K}(V,K)[/tex] and [tex]Hom_{K}(V \otimes V,K)[/tex]

where K is a field and V is a vector space over K.
 

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  • #2
quasar987
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This follows from the following elementary facts about tensors product that you should try to prove as easy exercices.

For V,W vectors spaces over K, and o the tensor product,

(1) Hom(V,W) is naturally isomorphic to V* o W
(2) V o K is naturally isomorphic to V
(3) (V o W)* is naturally isomorphic to V* o W*
 

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