
Conjugation of matrices.
def.: $\displaystyle SO(3)$ is the collection of lineair orthogonal transformations of $\displaystyle \mathbb{R}^3$
I want to show that two element of $\displaystyle SO(3) $ are conjugated if and only if they have the same trace.
(Maby you want to use: if $\displaystyle A \in SO(3) $ then $\displaystyle \exists\ p \in \mathbb{R}^3, p\neq 0$ and $\displaystyle Ap=p $)

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...
(Headbang)
I'll come back to it later if no one else tries to show it.
Cheers.