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Hermitian matrices

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data
    I don't understand why the Pauli matrix σx is hermitian. Nonetheless, I am able to prove why the σy matrix is hermitian.


    2. Relevant equations



    3. The attempt at a solution
    Whenever I do the transpose and then the conjugate I get the negative of σx instead. Am I doing something wrong or is this correct?
     
  2. jcsd
  3. Oct 26, 2011 #2

    vela

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    You're doing something wrong. Perhaps you don't have the correct matrix for [itex]\sigma_x[/itex].
     
  4. Oct 26, 2011 #3

    phyzguy

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    You're doing something wrong.
    [tex]\sigma_x = \left( \begin{array} \\0&1\\ \\1&0\\ \end{array} \right)[/tex]

    So when you transpose it it is the same. Since all of the elements are real, complex conjugation has no impact, so [tex] \sigma x = \sigma x ^\dagger[/tex]
     
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