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Dimension of a matrix vectorspace

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Let V be the vector space of n × m matrices with entried in a field F . What is the dimension of V ? Give an explicit basis for V over F .

    3. The attempt at a solution

    The question is a little vague, but if I understand correctly, wouldn't the dimension of V simply be n*m? For the basis (it has m*n elements), would it simply be zero matrices with a 1 in the "ij" entry, starting at 1,1 and ending at n,m?
    I feel like the question is just too easy, which is leading me to doubt my answer...
  2. jcsd
  3. Jan 13, 2012 #2


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    That seems correct.
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