The examples for the self adjoint eigensolver show the eigenvalues in increasing order. It this always the case? I did not see the order mentioned in the docs. Are complex eigenvalues ordered in increasing magnitude?

yes, for the self-adjoint solver the eigenvalues are always sorted in increasing order (as Lapack and MatLab do). For the non self-adjoint case, the eigen values are not sorted at all.

I'm updating the documentation to mention this.