Matrix problem

  • #1

Homework Statement



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.


Homework Equations





The Attempt at a Solution



No clue.
 

Answers and Replies

  • #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.
 
  • #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.
 
  • #4
Dick
Science Advisor
Homework Helper
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(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.

That's not such a big problem. Divide each one by two.
 
  • #5
That's not such a big problem. Divide each one by two.

How embarrassing.
 

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