Explore BrainMass
Share

Explore BrainMass

    Operator R(theta) for matrix representation

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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
    https://brainmass.com/math/algebra/operator-theta-matrix-representation-478807

    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.

    $2.19