This example computes all the eigenvalues and right eigenvectors of the matrix $A$, where The program first calls dgebal to balance the matrix; it then computes the Schur factorization of the balanced matrix, by reduction to Hessenberg form and the $QR$ algorithm. Then it calls dtrevc to compute the right eigenvectors of the balanced matrix, and finally calls dgebak to transform the eigenvectors back to eigenvectors of the original matrix $A$.