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Math Help - Conjugation of matrices.

  1. #1
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    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 )
    Last edited by bram kierkels; September 30th 2010 at 05:16 AM.
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  2. #2
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    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.
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