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Hermitian operator

  1. May 22, 2008 #1
    How do I show that an arbitrary operator A can be writte as A = B + iC where B and C are hermitian?
     
  2. jcsd
  3. May 22, 2008 #2
    Rewrite A as follows:

    [tex]A = \frac{(A+A^{\dagger})}{2} + \frac{(A-A^{\dagger})}{2}[/tex]

    Do you see why you can write A like that?
    And can you carry on?
     
    Last edited: May 22, 2008
  4. May 22, 2008 #3

    mathwonk

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    anytime anywhere you have an involution J you can alwaYS WRiTE ANYTHIng AS

    x = (x+JX)/2 + (X-JX)/2,

    where X+JX is invariant under J, and X-JX is anti-invariant under J.

    this is what lies beneath this fact.
     
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