# Eigenvalue order

I notice that Sage orders $A.eigenvalues()$ from lowest to highest (ascending order). Where does this functionality come from? Is NUMPY used in the backend?

I am trying to understand how to diagonalize a real symmetric matrix $A$ with orthogonal $Q$ such that $Q^T A Q = D$ where $D$ is diagonal and always in a specific order (say ascending or descending).

The ordering of the eigenvalues has a meanoing if and only if all these values belong in a "reasonably ordered" set. What do you think of complex eigenvalues ? and what about :

HTH,