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Results tagged with lie-groups
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user 4213
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
15
votes
Can SO_n(R) be approximated arbitrarily well using a discrete subgroup?
The only finite subgroups of $G=SO_3(\mathbf{R})$ are cyclic,
dihedral or of order 12, 24 or 60. The latter three can't work
for small enough $\epsilon$ but neither can the cyclic or dihedral
groups a …
- 20.8k
12
votes
Accepted
Parametrization of O(3)
The general element is $\pm\exp(A)$ where $A$ is skew-symmetric.
(This gives each element infinitely often). This trick essentially
works for all compact Lie groups.
There is also the Cayley paramete …
- 20.8k