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.
Classification of irreducible symmetric spaces which admit standard compact Clifford--Klein forms
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CURRENT FILTERING IN A THREE-PHASE THREE-WIRE POWER SYSTEM AT ASYMMETRIC SINUSOIDAL VOLTAGES
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.
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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.
Homotheties of a Class of Spherically Symmetric Space-Time Admitting [G.sub.3] as Maximal Isometry Group
Solution 4: The following is the fourth solution which has the maximum Noether symmetries for the plane symmetric static conformal Minkowski spacetime
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3.1.1 The O(2) symmetric positive solution branch by [lambda] continuation
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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].
The Structure of Symmetric Solutions of the Matrix Equation AX = B over a Principal Ideal Domain
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.
Orthogonal Symmetries and Reflections in Banach Spaces
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.
A Design of Functional Layer with Robust Constitutive Parameters for Multilayer Metamaterials

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