Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Duality_(mathematics)> ?p ?o }
- Duality_(mathematics) abstract "In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself. For example, Desargues' theorem is self-dual in this sense under the standard duality in projective geometry.In mathematical contexts, duality has numerous meanings although it is "a very pervasive and important concept in (modern) mathematics" and "an important general theme that has manifestations in almost every area of mathematics".Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars. For instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated test functions corresponds to the pairing in which one integrates a distribution against a test function, and Poincaré duality corresponds similarly to intersection number, viewed as a pairing between submanifolds of a given manifold.From a category theory viewpoint, duality can also be seen as a functor, at least in the realm of vector spaces. There it is allowed to assign to each space its dual space and the pullback construction allows to assign for each arrow f: V → W, its dual f∗: W∗ → V∗.".
- Duality_(mathematics) wikiPageExternalLink theories.
- Duality_(mathematics) wikiPageExternalLink pdfs.jsp?paperID=2887&mode=full.
- Duality_(mathematics) wikiPageExternalLink adt.html.
- Duality_(mathematics) wikiPageExternalLink CT90Como.pdf.
- Duality_(mathematics) wikiPageExternalLink S0273-0979-01-00913-2.
- Duality_(mathematics) wikiPageExternalLink 071218_conferencia_atiyah-d_article.pdf.
- Duality_(mathematics) wikiPageExternalLink 53.pdf.
- Duality_(mathematics) wikiPageExternalLink publications.html.
- Duality_(mathematics) wikiPageID "609737".
- Duality_(mathematics) wikiPageLength "46451".
- Duality_(mathematics) wikiPageOutDegree "284".
- Duality_(mathematics) wikiPageRevisionID "677120965".
- Duality_(mathematics) wikiPageWikiLink Abelian_group.
- Duality_(mathematics) wikiPageWikiLink Adjoint_functor.
- Duality_(mathematics) wikiPageWikiLink Adjoint_functors.
- Duality_(mathematics) wikiPageWikiLink Affine_scheme.
- Duality_(mathematics) wikiPageWikiLink Algebraic_Geometry_(book).
- Duality_(mathematics) wikiPageWikiLink Algebraic_closure.
- Duality_(mathematics) wikiPageWikiLink Algebraic_geometry.
- Duality_(mathematics) wikiPageWikiLink Antihomomorphism.
- Duality_(mathematics) wikiPageWikiLink Arithmetic.
- Duality_(mathematics) wikiPageWikiLink Arithmetics.
- Duality_(mathematics) wikiPageWikiLink Associative_algebra.
- Duality_(mathematics) wikiPageWikiLink Autonomous_category.
- Duality_(mathematics) wikiPageWikiLink Basis_(linear_algebra).
- Duality_(mathematics) wikiPageWikiLink Bilinear_form.
- Duality_(mathematics) wikiPageWikiLink Bilinear_function.
- Duality_(mathematics) wikiPageWikiLink Bilinear_map.
- Duality_(mathematics) wikiPageWikiLink Birkhoffs_representation_theorem.
- Duality_(mathematics) wikiPageWikiLink C*-algebra.
- Duality_(mathematics) wikiPageWikiLink CW_complex.
- Duality_(mathematics) wikiPageWikiLink Cambridge_University_Press.
- Duality_(mathematics) wikiPageWikiLink Cartesian_product.
- Duality_(mathematics) wikiPageWikiLink Categories_for_the_Working_Mathematician.
- Duality_(mathematics) wikiPageWikiLink Category:Duality_theories.
- Duality_(mathematics) wikiPageWikiLink Category_(mathematics).
- Duality_(mathematics) wikiPageWikiLink Category_theory.
- Duality_(mathematics) wikiPageWikiLink Cell_complex.
- Duality_(mathematics) wikiPageWikiLink Character_group.
- Duality_(mathematics) wikiPageWikiLink Circle_group.
- Duality_(mathematics) wikiPageWikiLink Closed_set.
- Duality_(mathematics) wikiPageWikiLink Closure_(topology).
- Duality_(mathematics) wikiPageWikiLink Cofibration.
- Duality_(mathematics) wikiPageWikiLink Coherent_duality.
- Duality_(mathematics) wikiPageWikiLink Coherent_sheaf.
- Duality_(mathematics) wikiPageWikiLink Coherent_sheaves.
- Duality_(mathematics) wikiPageWikiLink Cohomology.
- Duality_(mathematics) wikiPageWikiLink Colimit.
- Duality_(mathematics) wikiPageWikiLink Commutative_algebra.
- Duality_(mathematics) wikiPageWikiLink Commutative_ring.
- Duality_(mathematics) wikiPageWikiLink Compact-open_topology.
- Duality_(mathematics) wikiPageWikiLink Compact_group.
- Duality_(mathematics) wikiPageWikiLink Compact_space.
- Duality_(mathematics) wikiPageWikiLink Complement_(set_theory).
- Duality_(mathematics) wikiPageWikiLink Complete_Heyting_algebra.
- Duality_(mathematics) wikiPageWikiLink Complex_manifold.
- Duality_(mathematics) wikiPageWikiLink Complex_number.
- Duality_(mathematics) wikiPageWikiLink Computational_geometry.
- Duality_(mathematics) wikiPageWikiLink Constant_sheaf.
- Duality_(mathematics) wikiPageWikiLink Contravariant_functor.
- Duality_(mathematics) wikiPageWikiLink Converse_relation.
- Duality_(mathematics) wikiPageWikiLink Convex_hull.
- Duality_(mathematics) wikiPageWikiLink Convex_polyhedron.
- Duality_(mathematics) wikiPageWikiLink Convex_polytope.
- Duality_(mathematics) wikiPageWikiLink Convolution.
- Duality_(mathematics) wikiPageWikiLink Coproduct.
- Duality_(mathematics) wikiPageWikiLink De_Morgans_laws.
- Duality_(mathematics) wikiPageWikiLink De_Rham_cohomology.
- Duality_(mathematics) wikiPageWikiLink Delaunay_triangulation.
- Duality_(mathematics) wikiPageWikiLink Derived_category.
- Duality_(mathematics) wikiPageWikiLink Desargues_theorem.
- Duality_(mathematics) wikiPageWikiLink Differential_form.
- Duality_(mathematics) wikiPageWikiLink Differential_operator.
- Duality_(mathematics) wikiPageWikiLink Dimension_(vector_space).
- Duality_(mathematics) wikiPageWikiLink Dimension_formula.
- Duality_(mathematics) wikiPageWikiLink Direct_product.
- Duality_(mathematics) wikiPageWikiLink Direct_sum_of_groups.
- Duality_(mathematics) wikiPageWikiLink Discrete_group.
- Duality_(mathematics) wikiPageWikiLink Disjoint_union.
- Duality_(mathematics) wikiPageWikiLink Distribution_(mathematics).
- Duality_(mathematics) wikiPageWikiLink Distributive_lattice.
- Duality_(mathematics) wikiPageWikiLink Dual_(category_theory).
- Duality_(mathematics) wikiPageWikiLink Dual_abelian_variety.
- Duality_(mathematics) wikiPageWikiLink Dual_basis.
- Duality_(mathematics) wikiPageWikiLink Dual_code.
- Duality_(mathematics) wikiPageWikiLink Dual_cone.
- Duality_(mathematics) wikiPageWikiLink Dual_cone_and_polar_cone.
- Duality_(mathematics) wikiPageWikiLink Dual_graph.
- Duality_(mathematics) wikiPageWikiLink Dual_lattice.
- Duality_(mathematics) wikiPageWikiLink Dual_matroid.
- Duality_(mathematics) wikiPageWikiLink Dual_number.
- Duality_(mathematics) wikiPageWikiLink Dual_polyhedron.
- Duality_(mathematics) wikiPageWikiLink Dual_problem.
- Duality_(mathematics) wikiPageWikiLink Dual_space.
- Duality_(mathematics) wikiPageWikiLink Dual_vector_space.
- Duality_(mathematics) wikiPageWikiLink Duality_(electrical_circuits).
- Duality_(mathematics) wikiPageWikiLink Duality_(electrical_engineering).
- Duality_(mathematics) wikiPageWikiLink Duality_(mathematics).
- Duality_(mathematics) wikiPageWikiLink Duality_(optimization).