Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Dual_bundle> ?p ?o }
Showing triples 1 to 54 of
54
with 100 triples per page.
- 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 real, 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. This is not true in the case of complex vector bundles, for example the tautological line bundle over the Riemann sphere is not isomorphic to its dual.".
- Dual_bundle wikiPageID "7824691".
- Dual_bundle wikiPageLength "1482".
- Dual_bundle wikiPageOutDegree "22".
- Dual_bundle wikiPageRevisionID "641278680".
- Dual_bundle wikiPageWikiLink Associated_bundle.
- Dual_bundle wikiPageWikiLink Category:Vector_bundles.
- Dual_bundle wikiPageWikiLink Complex_vector_bundle.
- Dual_bundle wikiPageWikiLink Cotangent_bundle.
- Dual_bundle wikiPageWikiLink Differentiable_manifold.
- Dual_bundle wikiPageWikiLink Dual_representation.
- Dual_bundle wikiPageWikiLink Dual_space.
- Dual_bundle wikiPageWikiLink Fiber_bundle.
- Dual_bundle wikiPageWikiLink Fiber_bundle_construction_theorem.
- Dual_bundle wikiPageWikiLink Hausdorff_space.
- Dual_bundle wikiPageWikiLink Inner_product.
- Dual_bundle wikiPageWikiLink Inner_product_space.
- Dual_bundle wikiPageWikiLink Inverse_matrix.
- Dual_bundle wikiPageWikiLink Invertible_matrix.
- Dual_bundle wikiPageWikiLink Isomorphic.
- Dual_bundle wikiPageWikiLink Isomorphism.
- Dual_bundle wikiPageWikiLink Mathematics.
- Dual_bundle wikiPageWikiLink Natural_isomorphism.
- Dual_bundle wikiPageWikiLink Natural_transformation.
- Dual_bundle wikiPageWikiLink Paracompact.
- Dual_bundle wikiPageWikiLink Paracompact_space.
- Dual_bundle wikiPageWikiLink Structure_group.
- Dual_bundle wikiPageWikiLink Tangent_bundle.
- Dual_bundle wikiPageWikiLink Tautological_bundle.
- Dual_bundle wikiPageWikiLink Tautological_line_bundle.
- Dual_bundle wikiPageWikiLink Topology.
- Dual_bundle wikiPageWikiLink Transpose.
- Dual_bundle wikiPageWikiLink Vector_bundle.
- Dual_bundle wikiPageWikiLink Vector_space.
- Dual_bundle wikiPageWikiLinkText "Dual bundle".
- Dual_bundle wikiPageWikiLinkText "dual bundle".
- Dual_bundle wikiPageWikiLinkText "dual vector bundle".
- Dual_bundle wikiPageWikiLinkText "dual".
- Dual_bundle hasPhotoCollection Dual_bundle.
- Dual_bundle wikiPageUsesTemplate Template:Unreferenced.
- Dual_bundle subject Category:Vector_bundles.
- Dual_bundle hypernym *.
- Dual_bundle type Article.
- Dual_bundle type HistoricBuilding.
- Dual_bundle type Article.
- Dual_bundle type Bundle.
- 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 双対束.
- Dual_bundle sameAs m.026fc4t.
- Dual_bundle sameAs Q5310186.
- Dual_bundle sameAs Q5310186.
- Dual_bundle wasDerivedFrom Dual_bundle?oldid=641278680.
- Dual_bundle isPrimaryTopicOf Dual_bundle.