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Self-Dual


Self-dual describes an object A that is equal or isomorphic to its own dual, according to the notion of duality in use. A number of areas of mathematics have a notion of duality that can be applied to their objects.

For example, any normed space has a dual normed space. Hilbert spaces are self-dual normed 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 configurations, self-dual graphs, self-dual polyhedra, and self-dual codes.


See also

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

Portions of this entry contributed by Rasmus Hedegaard

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Cite this as:

Weisstein, Eric W., with contributions by Rasmus Hedegaard. "Self-Dual." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Self-Dual.html

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