1. For full detail, see exponential map SO ( 3 ). 2. It follows that the exponential map is compact subsets of. 3. Skew symmetric matrices generate orthogonal matrices with determinant 1 through the exponential map . 4. This can generate a exponential map , which can be used to rotate an object. 5. It the case of the Lorentz group, the exponential map is just the matrix exponential. 6. That this gives a one-parameter subgroup follows directly from properties of the exponential map . 7. A somewhat different way to think of the one-point compactification is via the exponential map . 8. Up to this exponential map , the global Cartan decomposition is the polar decomposition of a matrix. 9. Furthermore, your suggestion that the exponential map should point to this isomorphism also sounds eminently reasonable. 10. Thus the exponential map is a diffeomorphism from \ mathfrak { p } onto the space of positive definite matrices.
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