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 has the property that it is equal to its own dual, then 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.

Other examples of self-dual mathematical objects include self-dual graphs, self-dual polyhedra, self-dual
configurations, and self-dual codes.