Duality (mathematics)

Summary

In mathematics, a duality 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 $A$. In other cases the dual of the dual – the double dual or bidual – is not necessarily identical to the original (also called primal). 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.