Duality (mathematics)

A set C (blue) and its dual cone C* (red).

Hasse diagram of the power set of 1,2,3,4, partially ordered by ⊂. The dual poset, i.e. ordering by ⊃, is obtained by turning the diagram upside-down. The green nodes form an upper set and a lower set in the original and the dual order, respectively.

The features of the cube and its dual octahedron correspond one-for-one with dimensions reversed.

A planar graph in blue, and its dual graph in red.

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.

单词	Selfdual
释义	Selfdual 英语百科 Duality (mathematics) 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.
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Selfdual

Duality (mathematics)