Solving Hermitian Matrix Homework: Pauli & σy

[nnan]

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?

 

[vela]

You're doing something wrong. Perhaps you don't have the correct matrix for $\sigma_x$.

 

[phyzguy]

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

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