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I am studying linear algebra by myself, and I came across the need to prove the following, for adjoints of linear maps:

  • ($f^\dagger)^\dagger=f$
  • $(f\circ g)^\dagger=g^\dagger\circ f^\dagger$
  • $\langle v|fw\rangle=\langle f^\dagger v|w\rangle$

    Thank you very much!

    • 1
      The third is usually the *definition* of the adjoint. What is your definition?2012-10-26

    1 Answers 1

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    Meanwhile this was asked on MO and has an accepted answer: https://mathoverflow.net/questions/110739/