exponential map वाक्य
उदाहरण वाक्य
मोबाइल
- The exponential map of a nilpotent Lie algebra is a diffeomorphism between the Lie algebra and the unique associated connected, simply-connected Lie group.
- These also generate rotations through the exponential map, but instead of trigonometric functions, hyperbolic functions are needed, which generates a rotor as follows:
- In the tangent space at any point on a quaternion Slerp curve, the inverse of the exponential map transforms the curve into a line segment.
- Over the real numbers ( or more generally any field of characteristic 0 ) the exponential map takes any nilpotent square matrix to a unipotent matrix.
- Only one quarter of this plane is the image of the exponential map, so the logarithm is only defined on that quarter ( quadrant ).
- That is to say, the starting point p \ in H goes to the tangent plane from H through the inverse of the exponential map.
- :I'd guess the OP wants something for binomials like the exponential map formula for Lie groups, but that's fairly hairy.
- The exponential map is onto in each case, since the polynomial function lies in a given Lie subalgebra if and do and are sufficiently small.
- For an alternative derivation based on this exponential relationship, see Axis angle representation # Exponential map from so ( 3 ) to SO ( 3 ).
- Then travels from one tangent plane to the other through the isometry \ psi, and then down to the surface S'with another exponential map.
- The exponential is the exponential map, in this case the matrix exponential defined by putting the matrix into the usual power series for the exponential function.
- The exponential map is known not to be surjective in this case, even though it is surjective on the whole group " L ".
- Globally, the exponential map is not one-to-one, but in the case of the Lorentz group, it is surjective ( onto ).
- With some additional abuse of language, one notes that the exponential map provides a map from vectors in a tangent space to points in an underlying manifold.
- This can be generalised to all dimensions, with rotors, elements of the even subalgebra with unit magnitude, being generated by the exponential map from bivectors.
- The exponential map of a Lie group satisfies many properties analogous to those of the ordinary exponential function, however, it also differs in many important respects.
- In particular, cut locus of the exponential map is, roughly speaking, the set of all points where the exponential map fails to have a unique minimum.
- In particular, cut locus of the exponential map is, roughly speaking, the set of all points where the exponential map fails to have a unique minimum.
- In particular the exponential map is a polynomial mapping of \ mathfrak { n } onto " N ", with polynomial inverse given by the logarithm.
- A principal homogeneous space of is a manifold abstractly characterized by having a exponential map of the Lie algebra and in this way obtain, locally, a group action on.
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