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Math Help - Angle of rotation and axis of rotation of a 3x3 matrix

  1. #1
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    Angle of rotation and axis of rotation of a 3x3 matrix

    Hi,

    I've been given a matrix X which is a 3x3 rotation matrix entries 2/3 -2/3 -1/3
    1/3 2/3 -2/3
    2/3 1/3 2/3
    And I've found that [latex] X^6=I[/latex] Where I is the 3x3 identity matrix

    I'm then asked to find the angle of rotation and axis of rotation, however i have no idea how to do this, and also I haven't been told what axis it's rotating about... :S.

    Any help would be really appreciated thanks!.
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  2. #2
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    Re: Angle of rotation and axis of rotation of a 3x3 matrix

    the angle of rotation would be 2pi/6 = pi/3, because if 6 rotations are needed for a full rotation (no net effect = identity), then 6 times the angle of rotation = 2pi.
    I'm not sure about the axis of rotation though.

    EDIT: nvm I messed up. what I said is only true if X^6 = X, not X^6 = I, however, if X^6 = I, then X^7 = X, which means the angle of rotation is (2pi)/7 for similar reasons described above
    Last edited by HowDoIMath; April 14th 2013 at 08:38 AM. Reason: ERROR
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