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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
3
votes
1
answer
991
views
Lower bound for Jacobian of matrix exponential map near origin
What is a lower bound for the Jacobian of the exponential map from the skew-symmetric matrices to the orthogonal matrices near the origin?
3
votes
3
answers
471
views
Lower bound on the volume of a delta-ball in the orthogonal group O(n) of the type f(n)*delt...
Is there a lower bound on the volume of a delta-ball in the orthogonal group O(n) of the type
f(n) * delta^{n(n-1)/2}? For which f(n)? How can it be proven?
n(n-1)/2 is the number of degrees of freed …