How to show that orthogonal group is generated by rotations and permutations? Rotations are of the form $\begin{bmatrix}R&0\\0&I\end{bmatrix}$, where $R$ is $\begin{bmatrix}\cos\alpha&-\sin\alpha\\ \sin \alpha&\cos\alpha\end{bmatrix}$. Is there any reference on this?
2026-03-31 17:52:21.1774979541
How to show that orthogonal group is generated by rotations and permutations?
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Hint. To begin, think about how you can eliminate all but one entries on the first column by left-multiplying the matrix by Givens rotations.