---
tag: QS4283K3FK
kind: concept
name: Duality (mathematics)
aliases: [bidual, double-dual, dual-math, dual-mathematics, dual-maths, duality-math, duality-maths, duality-in-mathematics, duality-theorem, duality-theory, dualizing, mathematical-duality, self-dual, self-duality, selfdual]
sources:
  - wikipedia: en:609737@r1368642611
    locator: Duality (mathematics)
    note: adopted
    mention: wikipedia://en/609737
    sections: [Summary]
same_as:
  wikidata: Q1755512
  wikipedia: Duality (mathematics)
inventory: [AWX9DSX4D0]
---

## Summary

In mathematics, a **duality** translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a [[one-to-one|09NWETVTNY]] 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*.