# 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.

## 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.
References in periodicals archive ?
and the components which can be obtained from these by the symmetric properties.
If x = y, then we observe that M is a symmetric matrix.
R] with respect to a quarter symmetric non metric connection [nabla] and the curvature tensor R with respect to Riemannian connection D in LP-Sasakian manifolds are related as
Ahmad: Second order symmetric duality for nonlinear minimax mixed integer programming problems, Eur.
A natural next step is to consider symmetric matrices, which are (at least morally) a q-analogue of involutions, suggesting the possibility of interesting combinatorial results.
Because we take in consideration symmetric matrices it also means that [a.
The symmetric P-symmetric matrices were initially considered by Zhou, Hu and Zhang, associated with matrix equations and inverse eigenvalue problems, see[25, 26].
th] element of an n x n symmetric Toeplitz matrix [T.
Our goal is to link bijectively all these combinatorial symmetric structures thus showing they are counted by [omega.
Asymmetric Encryption differs from symmetric encryption in that uses two keys; a public key known to everyone and a private key, or secret key, known only to the recipient of the message.
The new price reduction is to apply to both connection and rental charges for BT Datastream Symmetric and BT IPstream Symmetric products and will see the standard connection charge for BT IPstream and Datastream Symmetric fall from GBP450 to GBP315.

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