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QUESTION

Find the eigenvalues of the rotation matrix

$$ A = \left[\begin{array}{rr}
 \cos\theta & -\sin\theta \\
 \sin\theta & \cos\theta \\
\end{array}\right].
$$

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ANSWER

The eigenvalues are $\cos\theta\pm i\sin\theta=e^{\pm i\theta}$.


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