A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal to its own dual, then A is said to be self-dual. For example, any normed vector space has a dual normed space. Hilbert spaces are self-dual normed vector spaces (up to isomorphism of Hilbert spaces). A geometric proposition is said to be self-dual when application of the duality principle of projective geometry results in a proposition equivalent to the original. Desargues' theorem is an example of a self-dual proposition.

duality principle | self-dual graph | self-dual polyhedron