<mathematics> 1. A relation R is symmetric if, for all x and y,
x R y => y R xIf 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.
(22 Sep 1996)