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Hermitian matrices

  • Thread starter nnan
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  • #1
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Homework Statement


I don't understand why the Pauli matrix σx is hermitian. Nonetheless, I am able to prove why the σy matrix is hermitian.


Homework Equations





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?
 

Answers and Replies

  • #2
vela
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You're doing something wrong. Perhaps you don't have the correct matrix for [itex]\sigma_x[/itex].
 
  • #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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