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.
(1996-09-22)
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Symbolics, Inc. « Symbol Manipulation Program «
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