Thread: Conjugation of matrices.

def.: is the collection of lineair orthogonal transformations of

I want to show that two element of are conjugated if and only if they have the same trace.

(Maby you want to use: if then and )

If A and B are conjugate then there exists an orthogonal transformation, such that:

A= CBC^t

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
CC^t=I).
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.

Cheers.