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 )

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- September 30th 2010, 04:58 AMbram kierkelsConjugation 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 ) - October 1st 2010, 06:03 AMInvisibleMan
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.