Definition:Symmetry


 * Relation Theory:
 * Symmetry (of a relation): whether a relation is symmetric, antisymmetric, asymmetric or non-symmetric.


 * Mapping Theory:
 * Symmetric Mapping: a mapping defined on a cartesian space whose values are preserved under permutation of its arguments:
 * $\map f {x_1, x_2, \dotsc, x_n} = \map f {x_{\map \pi 1}, x_{\map \pi 2}, \dotsc x_{\map \pi n} }$ for all permuations $\pi$ on $\set {1, 2, \dotsc n}$


 * Geometry:
 * Symmetry mapping: A movement of a geometric figure so that it looks the same after it has been moved.


 * Group Theory:
 * Symmetry group: The set of all symmetry mappings of a geometric figure, the operation being composition of mappings.


 * Linear Algebra:
 * Symmetric mapping
 * Symmetric matrix