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- 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 in projective geometry is self-dual in this sense.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.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∗.".
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- Duality_(mathematics) wikiPageExternalLink theories.
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- Duality_(mathematics) wikiPageExternalLink S0273-0979-01-00913-2.
- Duality_(mathematics) wikiPageExternalLink 071218_conferencia_atiyah-d_article.pdf.
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- Duality_(mathematics) wikiPageExternalLink 53.pdf.
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- Duality_(mathematics) wikiPageExternalLink CT90Como.pdf.
- Duality_(mathematics) wikiPageID "609737".
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- Duality_(mathematics) authorlink "Alexei Kostrikin".
- Duality_(mathematics) first "A. I.".
- Duality_(mathematics) hasPhotoCollection Duality_(mathematics).
- Duality_(mathematics) id "D/d034120".
- Duality_(mathematics) last "Kostrikin".
- Duality_(mathematics) title "Duality".
- Duality_(mathematics) subject Category:Duality_theories.
- Duality_(mathematics) type Abstraction100002137.
- Duality_(mathematics) type Cognition100023271.
- Duality_(mathematics) type DualityTheories.
- Duality_(mathematics) type Explanation105793000.
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- Duality_(mathematics) type Theory105989479.
- Duality_(mathematics) type Thinking105770926.
- Duality_(mathematics) comment "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.".
- Duality_(mathematics) label "Duality (mathematics)".
- Duality_(mathematics) label "Dualità (matematica)".
- Duality_(mathematics) label "Dualität (Mathematik)".
- Duality_(mathematics) label "Dualité (mathématiques)".
- Duality_(mathematics) label "Принцип двойственности".
- Duality_(mathematics) label "对偶 (数学)".
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- Duality_(mathematics) sameAs Dualità_(matematica).
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- Duality_(mathematics) sameAs Q1755512.
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- Duality_(mathematics) depiction Dual_Cube-Octahedron.svg.
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