# The DICT Development Group

**3 definitions found
for symmetric****From The Collaborative International Dictionary of English v.0.48 :
**
Symmetric \Sym*met"ric\, a.
Symmetrical.
[1913 Webster]

**From WordNet (r) 3.0 (2006) :
**
symmetric
adj 1: having similarity in size, shape, and relative position
of corresponding parts [syn: symmetrical, symmetric]
[ant: asymmetric, asymmetrical]

**From The Free On-line Dictionary of Computing (30 December 2018) :
**
symmetric
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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