***** original matrix ***** 1.00 2.00 300.00 4.00 5.00 2.00 3.00 400.00 5.00 6.00 3.00 4.00 5.00 6.00 7.00 4.00 5.00 600.00 7.00 8.00 5.00 6.00 700.00 8.00 9.00 ***** balance matrix ***** 1.00 2.00 37.50 4.00 5.00 2.00 3.00 50.00 5.00 6.00 24.00 32.00 5.00 48.00 56.00 4.00 5.00 75.00 7.00 8.00 5.00 6.00 87.50 8.00 9.00 ***** reduce to hessenberg form ***** 1.00e+00 3.94e+01 9.62e+00 3.33e+00 4.00e+00 2.40e+01 2.73e+01 1.16e+02 4.80e+01 4.80e+01 0.00e+00 8.55e+01 -4.78e+00 -1.33e+00 -2.00e+00 0.00e+00 0.00e+00 5.19e+00 1.45e+00 2.17e+00 0.00e+00 0.00e+00 0.00e+00 6.95e-08 4.77e-07