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Isomorphic diagonal matrix spaces

  1. Jun 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Is The space P2 is isomorphic to the space of all 3 × 3 diagonal matrices.

    2. Relevant equations



    3. The attempt at a solution
    I know that P2 is isomorphic to vectors with 3 components so i think this statement is true, is it?
     
  2. jcsd
  3. Jun 9, 2009 #2

    CompuChip

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    Re: isomorphism

    I think its true.
    An elegant way to prove it is to show that the space of vectors with n components is isomorphic to the space of n x n diagonal matrices.

    Then take n = 3 and compose isomorphisms :)
     
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