# Conjugation of matrices.

• September 30th 2010, 04:58 AM
bram kierkels
Conjugation of matrices.
def.: $SO(3)$ is the collection of lineair orthogonal transformations of $\mathbb{R}^3$

I want to show that two element of $SO(3)$ are conjugated if and only if they have the same trace.

(Maby you want to use: if $A \in SO(3)$ then $\exists\ p \in \mathbb{R}^3, p\neq 0$ and $Ap=p$)
• October 1st 2010, 06:03 AM
InvisibleMan
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...