exponential map वाक्य
उदाहरण वाक्य
मोबाइल
- The theorem holds also for Hilbert manifolds in the sense that the exponential map of a non-positively curved geodesically complete connected manifold is a covering map (; ).
- Conversely, the surjectivity of the exponential map, together with the above-mentioned block-diagonalization for skew-symmetric matrices, implies the block-diagonalization for orthogonal matrices.
- Take for example the complex plane under the exponential map : the image is "'C "'- { 0 }, which clearly is not simply connected.
- More precisely, in a nilpotent group satisfying this condition lattices correspond via the exponential map to lattices ( in the more elementary sense of Lattice ( group ) ) in the Lie algebra.
- On the open ball of this radius, the exponential map at " p " is a diffeomorphism from the tangent space to the manifold, and this is the largest such radius.
- The exponential map from the Lie algebra to the Lie group is not always " C " " Fr�chet space, even from arbitrary small neighborhood of 0 to corresponding neighborhood of 1.
- In general, the exponential map is only " locally defined ", that is, it only takes a small neighborhood of the origin at, to a neighborhood of in the manifold.
- The exponential map is one-to-one in a neighborhood of the identity in, hence the composition, where is the Lie algebra isomorphism, is onto an open neighborhood containing the identity.
- This difference can be traced to the properties of Frobenius automorphism and to the failure of the exponential map to establish a tight connection between properties of a modular Lie algebra and the corresponding algebraic group.
- Putting this into the Taylor series for the exponential map and using the property "'e 12 "'2 = " 1 results in a bivector version of Euler's formula,
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