# Operator R(theta) for matrix representation

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.

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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 ...

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

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