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Some hermitian operators relations

  1. Nov 7, 2011 #1
    How can I formally demonstrate this relations with hermitian operators?

    [tex](A^{\dagger})^{\dagger}=A [/tex]
    [tex](AB)^{\dagger}=B^{\dagger}A^{\dagger} [/tex]
    [tex]\langle x|A^{\dagger}y \rangle=\langle y|Ax \rangle ^*[/tex]
    [tex]If \ A \ is \ hermitian \ and \ invertible, \ then \ A^{-1} \ is \ hermitian[/tex]

    I've tried to prove them taking the definition of hermitian operator or/and considering matrices while operating, but I want something more formal.

    Last edited: Nov 7, 2011
  2. jcsd
  3. Nov 8, 2011 #2


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    Homework Helper

    how about using
    AA^{-1}= \mathbb{I}
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