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Exponential map (Lie theory) and Vector field

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Exponential map (Lie theory) and Vector field

Exponential map (Lie theory) vs. Vector field

In the theory of Lie groups, the exponential map is a map from the Lie algebra \mathfrak g of a Lie group G to the group, which allows one to recapture the local group structure from the Lie algebra. In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

Similarities between Exponential map (Lie theory) and Vector field

Exponential map (Lie theory) and Vector field have 7 things in common (in Unionpedia): Diffeomorphism, Geodesic, Lie algebra, Lie group, One-parameter group, Smoothness, Tangent space.

Diffeomorphism

In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.

Diffeomorphism and Exponential map (Lie theory) · Diffeomorphism and Vector field · See more »

Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

Exponential map (Lie theory) and Geodesic · Geodesic and Vector field · See more »

Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

Exponential map (Lie theory) and Lie algebra · Lie algebra and Vector field · See more »

Lie group

In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

Exponential map (Lie theory) and Lie group · Lie group and Vector field · See more »

One-parameter group

In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism from the real line \mathbb (as an additive group) to some other topological group G. That means that it is not in fact a group, strictly speaking; if \varphi is injective then \varphi(\mathbb), the image, will be a subgroup of G that is isomorphic to \mathbb as additive group.

Exponential map (Lie theory) and One-parameter group · One-parameter group and Vector field · See more »

Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

Exponential map (Lie theory) and Smoothness · Smoothness and Vector field · See more »

Tangent space

In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.

Exponential map (Lie theory) and Tangent space · Tangent space and Vector field · See more »

The list above answers the following questions

Exponential map (Lie theory) and Vector field Comparison

Exponential map (Lie theory) has 39 relations, while Vector field has 92. As they have in common 7, the Jaccard index is 5.34% = 7 / (39 + 92).

References

This article shows the relationship between Exponential map (Lie theory) and Vector field. To access each article from which the information was extracted, please visit:

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