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Tensor product

  1. Jul 23, 2010 #1
    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.
  2. jcsd
  3. Jul 23, 2010 #2


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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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