SetDirectory["/www/user/fdahl/papers/Conjugation/"];
<<kappaLib.m
<<Petrov.m

Class VIII: (6)

B=(({{0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}}));

V=(({{ lambda1, 1, 0, 0, 0, 0}, {0, lambda1, 1, 0, 0, 0}, {0, 0, lambda1, 1, 0, 0}, {0, 0, 0, lambda1, 1, 0}, {0, 0, 0, 0, lambda1, 1}, {0, 0, 0, 0, 0,  lambda1}}));

Eigenvalues[V]

W=eps1(({{0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0}}));

Eigenvalues[W]

S=(({{0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 0}, {eps1, 0, 0, 0, 0, 0}, {0, eps1, 0, 0, 0, 0}, {0, 0, eps1, 0, 0, 0}}));

Check that S is in set mathcal(S)

Transpose[S].B.S==W

Compute result

res=S.V.Inverse[S];
res//MatrixForm

Petrov[res]

Export notebook as .pdf

NotebookPrint[SelectedNotebook[],"/www/user/fdahl/papers/Conjugation/notebooks/ClassVIII.pdf"]