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