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Math Help - Proving Rotational Matrix Preserves Orientation

  1. #1
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    Angry Proving Rotational Matrix Preserves Orientation

    Hello,

    I'm trying to prove a specific lemma, one that shows that

    R(u X v) = Ru X Rv

    R \epsilonSO(3) is a special orthogonal rotation matrix;
    u,v \epsilon\Re^3 are vectors;
    and X is the cross product.

    Do I need to prove this using direct calculation, expanding and expanding.. I've tried and it gets quite large and unmanageable for me. Are there any other tricks I could try?
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  2. #2
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    Addendum

    It would also suffice to prove

    R(u X v) = det(R)(Ru X Rv)

    Since the det(R) = 1 for all R \epsilon SO(3)
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