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If X=[cosθsinθ−sinθcosθ]X = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}X=[cosθ−sinθsinθcosθ], then XXTXX^TXXT is
[0110]\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}[0110]
[−100−1]\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}[−100−1]
[1001]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}[1001]
[0−1−10]\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}[0−1−10]
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