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In mathematics, a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other. More formally, is antisymmetric precisely if for all
or equivalently, The definition of antisymmetry says nothing about whether actually holds or not for any . An antisymmetric relation on a set may be reflexive (that is, for all ), irreflexive (that is, for no ), or neither reflexive nor irreflexive. A relation is asymmetric if and only if it is both antisymmetric and irreflexive.Antisymmetric or skew-symmetric may refer to:
In mathematics, especially linear algebra, and in theoretical physics, the adjective antisymmetric (or skew-symmetric) is used for matrices, tensors, and other objects that change sign if an appropriate operation (e.g. matrix transposition) is performed. See: