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Homomorphism from Hom(W, F) to Hom(V, F)

  1. Mar 3, 2009 #1
    The problem statement, all variables and given/known data
    Let T be a homomorphism from V into W. Using T, define a homomorphism T* of Hom(W, F) into Hom(V, F).


    Note on notation
    Hom(V, F) is just the dual space of V. Similarly for Hom(W, F).


    The attempt at a solution
    This is a problem from Hernstein's "Topics in Algebra". It is given before the sections covering linear independence, bases and dual spaces, which I find odd. I don't have much to work with here. The only T* I can define at this point is the one sending everything in Hom(W, F) to the 0 functional in Hom(V, F). Any tips?
     
  2. jcsd
  3. Mar 3, 2009 #2

    Dick

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    Pick a w in Hom(W,F). So w:W->F. You want T*(w) to map V->F. There's a natural way to use T:V->W to do that.
     
  4. Mar 3, 2009 #3
    OOhhh....I see it know. Thanks a bunch.
     
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