- #1

ballzac

- 104

- 0

## Homework Statement

Show that

[tex]

\mathbf\alpha\equiv\left[\begin{array}{cc} 0&\mathbf\sigma\\ \mathbf\sigma&0\end{array}\right][/tex]

is hermitian.

## The Attempt at a Solution

My first instinct was to say that [tex]\mathbf\sigma[/tex] must be equal to its complex conjugate (as it would if it was a scalar and not a matrix). This is not the case, but I noticed that [tex]\sigma_y[/tex] is hermitian. The only way I can see it working (using the traditional definition of hermitian conjugate) is to treat [tex]\mathbf\alpha[/tex] as a set of three 4x4 matrices, two of which are real (and hence hermitian), and the other also being hermitian. Is this a valid interpretation of [tex]\mathbf\alpha[/tex]?