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Jan 26, 2016 at 17:25 comment added YCor In addition, since $O(3)$ is compact and does not contain zero, any subspace close enough to this given subspace still does not contain any orthogonal matrix. So the intersection is not generically non-empty.
Jan 26, 2016 at 10:40 history answered Roberto Pignatelli CC BY-SA 3.0