This question is in continuation to a previous question What are the Eigenvectors of the curl operator?. I know now that the curl operator \begin{bmatrix} 0 & -\frac{\partial}{\partial z} & \frac{\partial}{\partial y} \\ \frac{\partial}{\partial z} & 0 & -\frac{\partial}{\partial x} \\ -\frac{\partial}{\partial y} & \frac{\partial}{\partial x} & 0 \\ \end{bmatrix}is hermitian(http://www.eng.fsu.edu/~dommelen/quantum/style_a/curlherm.html). This should mean that the eigenvalues of this operator should be purely real. We can check this as $\vec{B} = (cos\ z, -sin\ z, 0)$ is an eigenvector with eigenvalue 1. However, $\vec{B} = e^y(1, 0, -i)$ is also an eigenvector with eigenvalue -i. What am I missing here?
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