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.

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

See also

Duality Principle, Self-Dual Graph, Self-Dual Polyhedron

Portions of this entry contributed by Rasmus Hedegaard

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Cite this as:

Hedegaard, Rasmus and Weisstein, Eric W. "Self-Dual." From MathWorld--A Wolfram Web Resource.

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