I have not seen a recent discussion of calculating eigenvalues and eigenvectors in Stan for a matrix that is not symmetric but is guaranteed of having real eigenvalues. Is such a calculation possible with the most recent version of Stan?
Hi,
this is quite out of my expertise, but since nobody else answered, I will give it a try. I don’t think this is currently supported, but I see at least two ways you might be able to make it happen (whether the computations would be quick and/or numerically stable is however unclear to me).

You should be able to implement the QR algorithm in pure Stan, as QR decomposition is available.

If you are OK with implementing your own C++ functions than you should be able to call the eigenvalues solver from the Eigen library (which Stan uses under the hood for most matrix computatoins)  most Eigen calls work out of the box with Stan’s autodiff types, so hopefully this one would as well. The relevant Eigen docs seem to be: Eigen: Eigenvalues module, while you might look at how Stan calls the QR decomposition functions (math/qr_Q.hpp at develop · standev/math · GitHub) to get an idea how the C++ code could look  it should be pretty straightforward.
Best of luck!