# 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 ?
When the order of the tensor is three and the tensor is symmetric in two modal dimensions, this is called the individual differences scaling (INDSCAL) model introduced by Carrol and Chang [4, 27].
The notion of weakly symmetric and weakly Ricci symmetric Riemannian manifolds were introduced by Tamassay ([15], [16]).
Penguin Computing's status as a premier HPC solutions provider is enhanced with the Symmetric Computing Trio product, said David Ingersoll, VP Sales for Penguin Computing.
Currently, Symmetric has the following plans: "PERSONAL" for free, "BASIC" for \$19/month, and "PRO" for \$99/month.
Beldiman: Higher-order symmetric multiobjective duality involving generalized (F, [rho], [gamma], b)-convexity, Rev.
From Pisarenko's work (Pisarenko, 1973) the problem of finding the smallest eigenvalue of a real symmetric, positive definite Toeplitz matrix (RSPDTM) plays an important role in signal processing.
In Section 4, we attack the general problem of enumerating symmetric matrices with zeroes on the diagonal with given rank.
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.
We assume parameterized spherically symmetric scattering length distributions [[rho].
In dimension four, mathematicians have long had a prime candidate for the best kissing arrangement: the 24-cell, a perfectly symmetric shape with 24 comers and 24 three-dimensional sides that are all regular octahedra.

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