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    Matrix and eigenvalues of a three-dimensional rotation

    P-UCLAB04S-08

    Area
    Prelim
    Seen at
    UCLA
    Years
    2004
    Status
    draft
    Contents

    Let \(T:\mathbb R^3\to\mathbb R^3\) be a rotation about the axis determined by \((1,0,-1)\) through an angle of \(30^\circ\); either orientation may be used.

    1. Find the matrix representation \(A\in M_3(\mathbb R)\) of \(T\) in the standard basis. You need not multiply out matrices, but you must evaluate inverses.

    2. Find all eigenvalues of \(A\) in \(M_3(\mathbb R)\).

    3. Find all eigenvalues of \(A\) when regarded as an element of \(M_3(\mathbb C)\).

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