Mathematics

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, 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''. * Alexander duality * Alvis–Curtis duality * Artin–Verdier duality * Beta-dual space * Coherent duality * Conjugate hyperbola * De Groot dual * Dual abelian variety * Dual basis in a field extension * Dual bundle * Dual curve *

Dual (category theory) In category theory, a branch of mathematics, duality is a correspondence between the properties of a category ''C'' and the dual properties of the opposite category ''C''op. Given a statement regarding the category ''C'', by interchanging the s ...

* Dual graph * Dual group *

Dual object In category theory, a branch of mathematics, a dual object is an analogue of a dual vector space from linear algebra for Object (category theory), objects in arbitrary Monoidal category, monoidal categories. It is only a partial generalization, base ...

* Dual pair * Dual polygon *

Dual polyhedron In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other ...

Dual problem In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then th ...

* Dual representation * Dual q-Hahn polynomials * Dual q-Krawtchouk polynomials *

Dual space In mathematics, any vector space ''V'' has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on ''V,'' together with the vector space structure of pointwise addition and scalar multiplication by cons ...

* Dual topology * Dual wavelet *

Duality (optimization) In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then th ...

Duality (order theory) In the mathematical area of order theory, every partially ordered set ''P'' gives rise to a dual (or opposite) partially ordered set which is often denoted by ''P''op or ''P'd''. This dual order ''P''op is defined to be the same set, but with ...

* Duality of stereotype spaces *

Duality (projective geometry) In projective geometry, duality or plane duality is a formalization of the striking symmetry of the roles played by Point (geometry), points and Line (geometry), lines in the definitions and theorems of projective planes. There are two approaches ...

* Duality theory for distributive lattices * Dualizing complex * Dualizing sheaf * Eckmann–Hilton duality * Esakia duality * Fenchel's duality theorem * Hodge dual * Isbell duality * Jónsson–Tarski duality * Lagrange duality * Langlands dual * Lefschetz duality * Local Tate duality *

Opposite category In category theory, a branch of mathematics, the opposite category or dual category C^ of a given Category (mathematics), category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal ...

* Poincaré duality ** Twisted Poincaré duality * Poitou–Tate duality * Pontryagin duality * S-duality (homotopy theory) * Schur–Weyl duality * Series-parallel duality * Serre duality * Spanier–Whitehead duality * Stone's duality * Tannaka–Krein duality * Verdier duality * Grothendieck local duality

Philosophy and religion

* Dualism (philosophy of mind) * Epistemological dualism *

Dualistic cosmology Dualism or dualistic cosmology is the moral or belief that two fundamental concepts exist, which often oppose each other. It is an umbrella term that covers a diversity of views from various religions, including both traditional religions and scri ...

* Soul dualism *

Yin and yang Originating in Chinese philosophy, yin and yang (, ), also yinyang or yin-yang, is the concept of opposite cosmic principles or forces that interact, interconnect, and perpetuate each other. Yin and yang can be thought of as complementary an ...

Engineering

Duality (electrical circuits) In electrical engineering, electrical terms are associated into pairs called duals. A dual of a relationship is formed by interchanging voltage and Electric current, current in an expression. The dual expression thus produced is of the same form ...

* Duality (mechanical engineering) * Observability/

Controllability Controllability is an important property of a control system and plays a crucial role in many regulation problems, such as the stabilization of unstable systems using feedback, tracking problems, obtaining optimal control strategies, or, simply p ...

control theory Control theory is a field of control engineering and applied mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the applic ...

Physics

* Complementarity (physics) * Dual resonance model * Duality (electricity and magnetism) *

Babinet's principle In physics, Babinet's principle states that the diffraction pattern from an opaque body is identical to that from an aperture (a hole in a screen) of the same size and shape except for the overall forward beam intensity. It was formulated in the ...

(electromagnetism) * Englert–Greenberger duality relation * Holographic duality ** AdS/CFT correspondence * Kramers–Wannier duality * Mirror symmetry ** 3D mirror symmetry * Montonen–Olive duality * Mysterious duality (M-theory) *

Seiberg duality In quantum field theory, Seiberg duality, conjectured by Nathan Seiberg in 1994, is an S-duality relating two different super QCD, supersymmetric QCDs. The two theories are not identical, but they agree at low energies. More precisely under a re ...

* String duality ** S-duality ** T-duality ** U-duality *

Wave–particle duality Wave–particle duality is the concept in quantum mechanics that fundamental entities of the universe, like photons and electrons, exhibit particle or wave (physics), wave properties according to the experimental circumstances. It expresses the in ...

Economics and finance

* Convex duality

References