Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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*
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook