The eigenvalues of a 180 degrees rotation matrix
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Show that if q is an element of Reals, then the operator T : Reals^2 -> Reals^2 given by
T ( x , y ) = ( x* cos q - y * sin q , x * sin q + y * cos q) has no real eignvalues unless T = I. I is identity.
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Solution Summary
The 2 pages solution demonstrates how to evaluate the eigenvalues of the transfromation matrix and to show that it becomes an identity or reflection matrix under certain conditions.
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