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Prove that Hermitian/Skew Herm/Unitary Matrix is a Normal Matrix

  1. Oct 14, 2008 #1
    1. The problem statement, all variables and given/known data
    Show the proof that the following are all Normal Matrices
    a. Hermitian
    b. Skew Hermitian
    c. Unitary

    2. Relevant equations

    Normal Matrices: A*A=AA*
    Hermitian Matrices: A=A* or aij=a*ji
    Skew Hermitian Matrices A=-A* or aij=-a*ji

    3. The attempt at a solution

    So far I have tried using the above information for Hermitian Matrices to try and prove that A*A=AA* but I keep getting answers I know not to be correct. I would appriciate a nudge in the correct direction so I can quit pulling my hair out. I have a feeling when I find the correct proof it will be quite obvious, but right now I am just missing something.
  2. jcsd
  3. Oct 14, 2008 #2


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    If A is hermitian then A*=A. A*A=AA=AA*. How are you trying to do it?
  4. Oct 14, 2008 #3
    I was trying to do it much more in depth using amn. It never occured to me to use the basic matrix itself. Like I said, it was right in front of me. Thank you for the help!
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