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    Operator R(theta) for matrix representation

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    Assume the operator R(theta) transforms a vector v (in two-dimensional real space) by swinging it around counterclockwise through an angle theta. How can I show that the operator R(theta) has the matrix representation

    cos(theta) -sin(theta)
    sin(theta) cos(theta)

    That is supposed to be a matrix.

    © BrainMass Inc. brainmass.com October 10, 2019, 4:49 am ad1c9bdddf

    Solution Preview

    Please see the attached files.

    The trick is to think about the rotation as rotation of the coordinate system clockwise while keeping the vector fixed (instead the other way around).
    Rotating ...

    Solution Summary

    The expert examines the operator R(theta) for matrix representation.