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Homework Help: Linear Algebra: Unitary matrix

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi

    My teacher told us that if we have a unitary matrix U, then

    [tex]
    \sum\limits_p {\left| {U_{np} } \right|^2 } = 1
    [/tex]

    Is that really correct? I thought he should be summing over n, not p.
     
  2. jcsd
  3. Jun 8, 2010 #2

    Dick

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    Use that if U is unitary, then the hermitian conjugate of U is unitary also to show you can sum over either index.
     
  4. Jun 8, 2010 #3
    Hmm, all I know is that U-1=UH. I cannot see how that helps me.
     
  5. Jun 8, 2010 #4

    Dick

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    Define V=U^H. Then V also satisfies V^(-1)=V^H. So V is also unitary. The sum over the second index for U is the same as the sum over the first index for V.
     
  6. Jun 8, 2010 #5
    I see, very smart. Thanks.

    Have a nice day.
     
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