symmetric


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symmetric

(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.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

symmetric

No difference in opposing modes. It typically refers to speed. For example, in symmetric operations, it takes the same time to compress and encrypt data as it does to decompress and decrypt it. Contrast with asymmetric.
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References in periodicals archive ?
Among all irreducible symmetric spaces [Br57], we prove that there are not many candidates for irreducible symmetric spaces G/H that admit standard compact Clifford Klein forms other than those listed in Theorem 1.7.
The transition from two-coordinate vectors in symmetric coordinates to three-coordinate complex vectors in phase coordinates is carried out by multiplying on the matrix [F.sub.0] - [parallel][[bar.e].sub.+] [[bar.e].sub.-][parallel].
The presented cylindrically symmetric spacetime (1) is conformally flat since the Weyl tensor vanishes, that is, [C.sub.[mu][nu][rho][sigma]] = 0, and static.
In this paper, we find homotheties of a class of the spherically symmetric space-time (5) admitting [G.sub.3] = SO(3) as the maximal isometry group for x(t, r) =2 ln r, imposing no restriction on the stress-energy tensor.
Solution 4: The following is the fourth solution which has the maximum Noether symmetries for the plane symmetric static conformal Minkowski spacetime
K., On pseudo cyclic Ricci symmetric manifolds admitting semi-symmetric connection, Scientia, series A : Math.
Table 2 showed 67.2% (119 casts) had symmetric canine relationship and 32.8% (58 casts) had asymmetric canine relationship.
3.1.1 The O(2) symmetric positive solution branch by [lambda] continuation
It is well known (see [7-9]) that (1) over F has a symmetric solution if and only if the equation AX = B has a solution and [AB.sup.T] = [BA.sup.T].
It follows from the previous lemma that one can find a Banach space X and a closed subspace H of X such that X is not weakly symmetric with respect to H.
As shown in Figure 1(d), the multilayer system is arranged in a BA-[(ABA).sup.m]-AB pattern, which has inside symmetric ABA blocks and outside asymmetric AB and BA blocks.