This example computes the $\alpha$ and $\beta$ arguments, which defines the generalized eigenvalues, of the matrix pair $\left(A,B\right)$ given by This requires calls to five routines: dggbal to balance the matrix, dgeqrf to perform the $QR$ factorization of $B$, dormqr to apply $Q$ to $A$, dgghrd to reduce the matrix pair to the generalized Hessenberg form and dhgeqz ( to compute the eigenvalues using the $QZ$ algorithm.