The exponential map from the Lie algebra su(2) of SU(2) to SU(2) is surjective, (for example, see my manuscript http://www.cis.upenn.edu/~jean/gbooks/manif.html <http://www.cis.upenn.edu/~jean/gbooks/manif.html>, Section 1.4), so it gives you a smooth parametrization of SU(2) in terms of three real parameters. Recall that su(2) is the set of skew hermitian matrices, ib c + id -c + id -ib with a, b, c real. I dont know if this is what you wanted. Best, — Jean Gallier
On Mar 15, 2018, at 6:51 PM, Henry Baker <hbaker1@pipeline.com> wrote:
We know that the circle group is enumerated uniformly by
cos(t)+i*sin(t), for i in [0,2*pi)
using a single (real) parameter t.
Is there a way of uniformly enumerating the unit quaternions * with 1 parameter (probably some sort of random walk) ? * with 2 parameters (probably some sort of random walk) ? * with 1 complex parameter ????? * with 3 parameters ???
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