1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook