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Symmetric Matrix as a subspace

  1. Nov 23, 2008 #1
    My question is;
    Let S = {A € Mn,n | A = AT } the set of all symmetric n × n matrices
    Show that S is a subspace of the vector space Mn,n

    I do not know how to start to this if you can give me a clue for starting, I appreciate.
     
  2. jcsd
  3. Nov 23, 2008 #2

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    What are the conditions that a subset be a subspace? It's not hard to show that S satisfies them.
     
  4. Nov 24, 2008 #3
    edit: A=A^T

    It must satisfies the operations in S and it requires that it must be closed under vector addition and scaler multiplication. I got it: symmetic matrix satisfies those condition :) thanks:)
     
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