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

Class VII: (111111)

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, 0, 0, 0, 0, 0}, {0, lambda2, 0, 0, 0, 0}, {0, 0, lambda3, 0, 0, 0}, {0, 0, 0, lambda4, 0, 0}, {0, 0, 0, 0,  lambda5, 0}, {0, 0, 0, 0, 0,  lambda6}}));

Eigenvalues[V]

W=(({{eps1, 0, 0, 0, 0, 0}, {0, eps2, 0, 0, 0, 0}, {0, 0, eps3, 0, 0, 0}, {0, 0, 0, eps4, 0, 0}, {0, 0, 0, 0, eps5, 0}, {0, 0, 0, 0, 0, eps6}}));

Eigenvalues[W]

W=W/.{eps1->-1,eps2->-1,eps3->-1,eps4->1,eps5->1,eps6->1};
W//MatrixForm
Eigenvalues[W]

S=Sqrt[2](({{-(1/2), 0, 0, (1/2), 0, 0}, {0, -(1/2), 0, 0, (1/2), 0}, {0, 0, -(1/2), 0, 0, (1/2)}, {(1/2), 0, 0, (1/2), 0, 0}, {0, (1/2), 0, 0, (1/2), 0}, {0, 0, (1/2), 0, 0, (1/2)}}));

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/ClassVII.pdf"]