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Sums of Subspaces

  1. Sep 23, 2009 #1
    If [tex]U_1, U_2, U_3,[/tex] are subspaces of V (over fields R and/or C), is the addition of the subspaces commutative and associative?

    To me it seems rather trivial .. Since their summation is simply the set of all possible sums of the elements of [tex]U_1, U_2, U_3[/tex], and the elements themselves are associative and commutative, then so must be their subspaces and their sum.

    Seems too easy to me ... I must be missing something ,,
  2. jcsd
  3. Sep 24, 2009 #2
    It is true. What you wrote is fine. But if you are doubtful, then you need to write it out more carefully.
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