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What (who) is symmetrize - definition
Symmetrize
·vt To make proportional in its parts; to reduce to symmetry.
symmetrical
![Symmetry (left) and [[asymmetry]] (right)](https://commons.wikimedia.org/wiki/Special:FilePath/Asymmetric (PSF).svg?width=200 "Symmetry (left) and [[asymmetry]] (right)")
![A [[fractal]]-like shape that has [[reflectional symmetry]], [[rotational symmetry]] and [[self-similarity]], three forms of symmetry. This shape is obtained by a [[finite subdivision rule]].](https://commons.wikimedia.org/wiki/Special:FilePath/BigPlatoBig.png?width=200 "A [[fractal]]-like shape that has [[reflectional symmetry]], [[rotational symmetry]] and [[self-similarity]], three forms of symmetry. This shape is obtained by a [[finite subdivision rule]].")
![Great Mosque of Kairouan]] also called the Mosque of Uqba, in [[Tunisia]].](https://commons.wikimedia.org/wiki/Special:FilePath/Great Mosque of Kairouan, west portico of the courtyard.jpg?width=200 "Great Mosque of Kairouan]] also called the Mosque of Uqba, in [[Tunisia]].")
![The ceiling of [[Lotfollah mosque]], [[Isfahan]], [[Iran]] has 8-fold symmetries.](https://commons.wikimedia.org/wiki/Special:FilePath/Isfahan Lotfollah mosque ceiling symmetric.jpg?width=200 "The ceiling of [[Lotfollah mosque]], [[Isfahan]], [[Iran]] has 8-fold symmetries.")
![Clay pots thrown on a [[pottery wheel]] acquire rotational symmetry.](https://commons.wikimedia.org/wiki/Special:FilePath/Makingpottery.jpg?width=200 "Clay pots thrown on a [[pottery wheel]] acquire rotational symmetry.")
![A spherical [[symmetry group]] with [[octahedral symmetry]]. The yellow region shows the [[fundamental domain]].](https://commons.wikimedia.org/wiki/Special:FilePath/Sphere symmetry group o.svg?width=200 "A spherical [[symmetry group]] with [[octahedral symmetry]]. The yellow region shows the [[fundamental domain]].")
![[[Leonardo da Vinci]]'s '[[Vitruvian Man]]' (ca. 1487) is often used as a representation of symmetry in the human body and, by extension, the natural universe.](https://commons.wikimedia.org/wiki/Special:FilePath/Studio del Corpo Umano - Leonardo da Vinci.png?width=200 "[[Leonardo da Vinci]]'s '[[Vitruvian Man]]' (ca. 1487) is often used as a representation of symmetry in the human body and, by extension, the natural universe.")
![Seen from the side, the [[Taj Mahal]] has bilateral symmetry; from the top (in plan), it has fourfold symmetry.](https://commons.wikimedia.org/wiki/Special:FilePath/Taj Mahal, Agra views from around (85).JPG?width=200 "Seen from the side, the [[Taj Mahal]] has bilateral symmetry; from the top (in plan), it has fourfold symmetry.")
![The [[triskelion]] has 3-fold rotational symmetry.](https://commons.wikimedia.org/wiki/Special:FilePath/The armoured triskelion on the flag of the Isle of Man.svg?width=200 "The [[triskelion]] has 3-fold rotational symmetry.")
![p4 symmetry]]](https://commons.wikimedia.org/wiki/Special:FilePath/Zoomorphs.svg?width=200 "p4 symmetry]]")
STATE; BALANCE OF OBJECT
Symmetries; Symmetric; Symmetrical; Symmetry transformation; Symmetry principles; Symettry; Symmetry and asymmetry; Planar symmetry; Symmetric property; Chemical symmetry elements; Symetrical; Symmetry (music); ⌯; Quadrilateral symmetry; Musical symmetry
adj. symmetrical to, with
symmetric
STATE; BALANCE OF OBJECT
Symmetries; Symmetric; Symmetrical; Symmetry transformation; Symmetry principles; Symettry; Symmetry and asymmetry; Planar symmetry; Symmetric property; Chemical symmetry elements; Symetrical; Symmetry (music); ⌯; Quadrilateral symmetry; Musical symmetry
<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)
