Once trying to solve a generalized eigenvalue problem using scipy's algorithms I encountered an option homogenous_eigvals in the solver. The documentation says only that, once it's applied, the algorithm returns a pair of numbers instead one, fulfilling
w[1,i] a vr[:,i] = w[0,i] b vr[:,i]
with w -- eigvals, vr -- eigvectors, a, b -- matrices defining the problem. I.e the eigenvals of the original problem are ratios of the homogenous ones. However it is not mentioned what is the use of such representation. It is also not clear if there is a different algorithm involved in computing those... Can someone please help me with a reference of what those homogenous eigenvalues are and how are they computed? Cheers!