It's really just a floating point precision issue. Even if you represented the input matrix as a rational elementary type the output eigenvalues would be a subs

It's really just a floating point precision issue. Even if you represented the input matrix as a rational elementary type the output eigenvalues would be a subset of the reals and calculated as being floating point. You could get around it if you had a special matrix type where you knew you were definitely going to get rational eigenvalues and you could dispatch on that type.