Symmetric



adjective
1.
characterized by or exhibiting symmetry; well-proportioned, as a body or whole; regular in form or arrangement of corresponding parts.
2.
Geometry.

noting two points in a plane such that the line segment joining the points is bisected by an axis:
Points (1, 1) and (1, −1) are symmetrical with respect to the x-axis.
noting a set consisting of pairs of points having this relation with respect to the same axis.
noting two points in a plane such that the line segment joining the points is bisected by a point or center:
The points (1, 1) and (−1, −1) are symmetrical with respect to (0, 0).
noting a set consisting of pairs of points having this relation with respect to the same center.

3.
Often, symmetric. Mathematics.

noting a square matrix that is equal to its transpose.
noting a dyad or dyadic that is equal to its conjugate.
noting a relation in which one element in relation to a second implies the second in relation to the first.

4.
Botany.

divisible into two similar parts by more than one plane passing through the center; actinomorphic.
(of a flower) having the same number of parts in each whorl.

5.
Chemistry.

having a structure that exhibits a regular repeated pattern of the component parts.
noting a benzene derivative in which three substitutions have occurred at alternate carbon atoms.

6.
affecting corresponding parts simultaneously, as certain diseases.
adjective
1.
(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
2.
another word for symmetrical (sense 5)
adjective
1.
possessing or displaying symmetry Compare asymmetric
2.
(maths)

(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

3.
(chem) (of a compound) having a molecular structure in which substituents are symmetrical about the molecule
4.
(botany) another word for isomerous
5.
Also symmetric. (of a disease, infection, etc) affecting both sides of the body or corresponding parts, such as both legs
symmetric (sĭ-mět’rĭk) or symmetrical
(sĭ-mět’rĭk)

Relating to or exhibiting symmetry.

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)

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