Hello Dan. Strictly spoken I sum not over generators, but over the whole group. That is the trick that

Conjugate[T[a]] . H . T[a] equals H.

The details are outlined in the text cited.

Correction: it must be of course

TransposeConjugate[T[a]] . H . T[a] equals H.

Very nice. I have a question though. You create a new matrix by summing the generators and orthogonalize this new one. How do you know the transform will then simultaneously orthogonalize each summand? Does this come from the theory?

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