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Matrix problem

  1. Jul 9, 2009 #1
    1. The problem statement, all variables and given/known data

    An nxn matrix C is skew symmetric if C^t = -C. Prove that every square matrix A can be written uniquely as A = B + C where B is symmetric and C is skew symmetric.


    2. Relevant equations



    3. The attempt at a solution

    No clue.
     
  2. jcsd
  3. Jul 9, 2009 #2

    Dick

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    You aren't trying very hard, now are you? Tell me about (A+A^T) and (A-A^T). Are they symmetric, skew-symmetric or neither? You have to help here.
     
  4. Jul 12, 2009 #3
    (A+A^T)is symmetric, (A-A^T)is skew symmetric, but adding them together produces 2A, not A. I'm not sure what to do with this information.
     
  5. Jul 12, 2009 #4

    Dick

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    That's not such a big problem. Divide each one by two.
     
  6. Jul 12, 2009 #5
    How embarrassing.
     
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