Eigenvalue Issues of rate matrixes

Dear aaronjg and Daniel Simpson,
thanks for Answering almost three years ago. I finally worked with the matrix exponential and created a model for a hidden stochastic chemical Network within the Kalman filter framework
Preprint on: Model selection for hidden Markov/Kalman filter/ chemical Master equation models. But know I am coming back to this question here since I would really like to use prior information on the expected time scales (eigenvalues) of the process. Have you done something on that before is there an easier way then what SPD Pencil and Pseudo spectra…

Basically I have samples from rate matrix which by construction has real valued eigenvalues but it is not in a symmetric form. Any solutions to calculate the eigenvalues in order to put some prior on it.

Jan