antisymmetric
A relation on is antisymmetric iff , . For a finite set with elements, the number of possible antisymmetric relations is out of the total possible relations.
Antisymmetric is not the same thing as “not symmetric”, as it is possible to have both at the same time. However, a relation that is both antisymmetric and symmetric has the condition that . There are only such possible relations on .
An example of an antisymmetric relation on would be . One relation that isn’t antisymmetric is because we have both and , but
Title | antisymmetric |
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Canonical name | Antisymmetric |
Date of creation | 2013-03-22 12:15:50 |
Last modified on | 2013-03-22 12:15:50 |
Owner | aoh45 (5079) |
Last modified by | aoh45 (5079) |
Numerical id | 14 |
Author | aoh45 (5079) |
Entry type | Definition |
Classification | msc 03E20 |
Synonym | antisymmetry |
Related topic | Reflexive |
Related topic | Symmetric |
Related topic | ExteriorAlgebra |
Related topic | SkewSymmetricMatrix |