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Is this an isomorphism between vector spaces

  1. Apr 22, 2009 #1
    1. The problem statement, all variables and given/known data
    a belongs to R
    show that the map
    L: R^n------R^n>0
    (R^n>0 denote the n-fold cartesian product of R>0 with itself)
    (a1)
    (....) ----------
    (an)

    (e^a1)
    (.....)
    (e^an)
    is a isomorphism between the vector space R^n and the vector space R^n>0

    2. Relevant equations



    3. The attempt at a solution
    no idea about this question
    any clue ?
    can i say because of bijective
    a1=e^a1 .......an=e^an ??
     
  2. jcsd
  3. Apr 22, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: isomorphism

    I don't get the question. Yes, it is a bijection. But I wouldn't think of (R>0)^n as a vector space in the usual sense. If there's a bijection between two sets you can always say one is the same as the other just by identifying operations in one with operations in the other. But I doubt that's what the question is.
     
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