(logic, maths) (of a relation) holding between a pair of arguments x and y when and only when it holds between y and x, as … is a sibling of … but not … is a brother of …Compare asymmetric (sense 5), antisymmetric, nonsymmetric
possessing or displaying symmetry Compare asymmetric
(of two points) capable of being joined by a line that is bisected by a given point or bisected perpendicularly by a given line or plane: the points (x, y) and (–x, –y) are symmetrical about the origin
(of a configuration) having pairs of points that are symmetrical about a given point, line, or plane: a circle is symmetrical about a diameter
(of an equation or function of two or more variables) remaining unchanged in form after an interchange of two variables: x + y = z is a symmetrical equation
(chem) (of a compound) having a molecular structure in which substituents are symmetrical about the molecule
Relating to a logical or mathematical relation between two elements such that if the first element is related to the second element, the second element is related in like manner to the first. The relation a = b is symmetric, whereas the relation a > b is not.
mathematics 1. A relation R is symmetric if, for all x and y, x R y => y R x If it is also antisymmetric (x R y & y R x => x == y) then x R y => x == y, i.e. no two different elements are related. 2. In linear algebra, a member of the tensor product of a vector space with itself one or more times, is symmetric if it is a fixed point of all of the linear isomorphisms of the tensor product generated by permutations of the ordering of the copies of the vector space as factors. It is said to be antisymmetric precisely if the action of any of these linear maps, on the given tensor, is equivalent to multiplication by the sign of the permutation in question. (1996-09-22)