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Structure of elements of the unitary group

  1. Apr 12, 2009 #1
    Hey guys,

    I'm having a massive brain freeze here trying to show that for any element g in the unitary group you can always represent it as s*some diagonal matrix*s^-1. The only requirement for an element to be unitary is that its hermitian conjugate is its inverse correct? Any hints/help would be appreciated!

    Cheers
    -G
     
    Last edited: Apr 12, 2009
  2. jcsd
  3. Apr 12, 2009 #2
  4. Apr 13, 2009 #3
    Ah i think i see what youre saying, its kind of a basis transformation thing? I sort of understand that (not in a way to provide a proper proof though) but is there a way to arrive at that relation just from the strict definition of a unitary matrix?

    Cheers
    -G
     
  5. Apr 13, 2009 #4
    It inevitably follows from a theorem in Linear algebra that states every unitary matrix is diagonalizable. You can probably find it in some L(Alg) textbook or alternatively you can simply google that statement.
     
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