If A and B are conjugate then there exists an orthogonal transformation, such that:
Prove that Tr(CBC^t)=Tr(B) (by definition).
(or if you want you can use the next identity, Tr(AB)=Tr(BA), and the fact that
Now I can't recall how to show that Tr A =Tr B yields A=CBC^t...
I'll come back to it later if no one else tries to show it.