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Hermitian matrices and unitary similarity transformations

  1. Feb 1, 2012 #1

    ShayanJ

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    I tried to prove that a hermitian matrix remains hermitian under a unitary similarity transformation.I just could do it to he point shown below.Any ideas?

    [itex] [ ( U A U ^ {\dagger}) B ] ^ {\dagger} = B ^ {\dagger} (U A U ^ {\dagger}) ^ {\dagger} = B (U A^ {\dagger} U ^ {\dagger}) [/itex]

    thanks
     
  2. jcsd
  3. Feb 1, 2012 #2

    tiny-tim

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    Hi Shyan! :smile:

    What's B doing there? :confused:
     
  4. Feb 1, 2012 #3

    ShayanJ

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    Isn't B the hermitian matrix which should remain hermitian?
     
  5. Feb 1, 2012 #4

    tiny-tim

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    But A is the matrix which undergoes the similarity transformation.
     
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