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- Dual_bundle abstract "In mathematics, the dual bundle of a vector bundle π : E → X is a vector bundle π* : E* → X whose fibers are the dual spaces to the fibers of E. The dual bundle can be constructed using the associated bundle construction by taking the dual representation of the structure group.Specifically, given a local trivialization of E with transition functions tij, a local trivialization of E* is given by the same open cover of X with transition functions tij* = (tijT)−1 (the inverse of the transpose). The dual bundle E* is then constructed using the fiber bundle construction theorem.For example, the dual to the tangent bundle of a differentiable manifold is the cotangent bundle.If the base space X is paracompact and Hausdorff then a finite-rank vector bundle E and its dual E* are isomorphic as vector bundles. However, just as for vector spaces, there is no canonical choice of isomorphism unless E is equipped with an inner product.".
- Dual_bundle wikiPageID "7824691".
- Dual_bundle wikiPageRevisionID "417750971".
- Dual_bundle hasPhotoCollection Dual_bundle.
- Dual_bundle subject Category:Vector_bundles.
- Dual_bundle type Abstraction100002137.
- Dual_bundle type Collection107951464.
- Dual_bundle type Group100031264.
- Dual_bundle type Package108008017.
- Dual_bundle type VectorBundles.
- Dual_bundle comment "In mathematics, the dual bundle of a vector bundle π : E → X is a vector bundle π* : E* → X whose fibers are the dual spaces to the fibers of E. The dual bundle can be constructed using the associated bundle construction by taking the dual representation of the structure group.Specifically, given a local trivialization of E with transition functions tij, a local trivialization of E* is given by the same open cover of X with transition functions tij* = (tijT)−1 (the inverse of the transpose).".
- Dual_bundle label "Dual bundle".
- Dual_bundle sameAs m.026fc4t.
- Dual_bundle sameAs Q5310186.
- Dual_bundle sameAs Q5310186.
- Dual_bundle sameAs Dual_bundle.
- Dual_bundle wasDerivedFrom Dual_bundle?oldid=417750971.
- Dual_bundle isPrimaryTopicOf Dual_bundle.