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Math Help - Matrix Transformations Help

  1. #1
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    Matrix Transformations Help

    Sorry I'm new to this topic and attempting to self teach can anyone give me an idiots guide to this question

    The Matrix \begin{bmatrix}0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 0 & 0\end{bmatrix} represents a rotation.

    Find the equation of the axis of rotation and what is the angle of the rotation


    many thanks

    Simon
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  2. #2
    Moo
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    Hello,

    The axis is generated by the eigenvector associated to the eigenvalue 1.

    AX=X

    \begin{pmatrix} 0&1&0 \\ 0&0&1 \\ 1&0&0 \end{pmatrix} \begin{pmatrix} x_1\\x_2\\x_3 \end{pmatrix}=\begin{pmatrix} x_1\\x_2\\x_3 \end{pmatrix}

    Solve for x_1, ~x_2, ~x_3

    hmmm I'm sorry I don't remember how to find the angle >.<
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  3. #3
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    This questions requires a decent 3D drawing.

    Notice that \begin{pmatrix} 0&1&0 \\ 0&0&1 \\ 1&0&0 \end{pmatrix} \begin{pmatrix} i\\j\\k \end{pmatrix}=\begin{pmatrix} k\\i\\j \end{pmatrix}

    Your swapping the axis around in order, so the line must be \begin{pmatrix} 1\\1\\1 \end{pmatrix} and the angle is 120 degrees (as  A^3 = I )

    Bobak
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