Eigenvalue decomposition of a positive-definite Hermitian matrix is a special case of SVD. However, svd returns the singular values in descending order, where as eig returns them in ascending order. The order of singular values is fixed popular convention, so I think for consistency eig should adhere to the same order.

Further more, I would prefer the ordering for eig to be descending absolute value. This would also make it consistent with the default behavior of eigs and with the fact that singular values of Hermitian matrices are the absolute values of the eigenvalues.

I don't know how this would affect perfomance, i.e. can LAPACK do this for us naturally or would we need to sort (and permute the eigenvectors) afterwards.