NAG Library Manual, Mark 28.6
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F08YKF Example Program Results
Matrix A after balancing
1       2       3       4       5
1   1.0000  1.0000  0.1000  0.1000  0.1000
2   2.0000  4.0000  0.8000  1.6000  3.2000
3   0.3000  0.9000  0.2700  0.8100  2.4300
4   0.4000  1.6000  0.6400  2.5600 10.2400
5   0.5000  2.5000  1.2500  6.2500 31.2500

Matrix B after balancing
1       2       3       4       5
1   1.0000  2.0000  0.3000  0.4000  0.5000
2   1.0000  4.0000  0.9000  1.6000  2.5000
3   0.1000  0.8000  0.2700  0.6400  1.2500
4   0.1000  1.6000  0.8100  2.5600  6.2500
5   0.1000  3.2000  2.4300 10.2400 31.2500

Matrix A in Hessenberg form
1       2       3       4       5
1  -2.1898 -0.3181  2.0547  4.7371 -4.6249
2  -0.8395 -0.0426  1.7132  7.5194-17.1850
3   0.0000 -0.2846 -1.0101 -7.5927 26.4499
4   0.0000  0.0000  0.0376  1.4070 -3.3643
5   0.0000  0.0000  0.0000  0.3813 -0.9937

Matrix B in Hessenberg form
1       2       3       4       5
1  -1.4248 -0.3476  2.1175  5.5813 -3.9269
2   0.0000 -0.0782  0.1189  8.0940-15.2928
3   0.0000  0.0000  1.0021-10.9356 26.5971
4   0.0000  0.0000  0.0000  0.5820 -0.0730
5   0.0000  0.0000  0.0000  0.0000  0.5321

Minimal required LWORK =      5
Actual value of  LWORK =     30

Generalized eigenvalues

1     ( -2.437,  0.000)
2     (  0.607,  0.795)
3     (  0.607, -0.795)
4     (  1.000,  0.000)
5     ( -0.410,  0.000)

Right eigenvectors
1       2       3       4       5
1  -0.3083  0.7026  0.0000 -0.3985 -0.3747
2   0.6622 -0.5582 -0.3678  0.7287  0.7339
3  -0.6244  0.1600  0.1763 -0.5380 -0.5394
4   0.2732 -0.0211 -0.0492  0.1423  0.1720
5  -0.0438  0.0010  0.0072 -0.0199 -0.0192

Left eigenvectors
1       2       3       4       5
1  -0.3747  0.7026  0.0000 -0.3985  0.3083
2   0.7339 -0.5582 -0.3678  0.7287 -0.6622
3  -0.5394  0.1600  0.1763 -0.5380  0.6244
4   0.1720 -0.0211 -0.0492  0.1423 -0.2732
5  -0.0192  0.0010  0.0072 -0.0199  0.0438
```