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Dimensionality proof

  1. Feb 18, 2008 #1
    1. The problem statement, all variables and given/known data Prove that the subspace of a finite dimensional vector space is finite dimensional

    2. Relevant equations dim(V)=#basis vectors

    3. The attempt at a solution
    I was thinking about making a summation of the basis vectors in the vector space and the subtracting the summation of the basis vectors in the subspace. That way I get a finite# of basis vectors left over. But that thinking turned out to be flawed because I'm assuming that the #of basis vectors in the subspace is finite(what I'm trying to prove). So I'm back to square 1.
  2. jcsd
  3. Feb 18, 2008 #2


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    Can a finite-dimensional space have infinitely many linearly independent vectors?
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