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symmetric a. 對稱的;保持均衡的 對稱的;保持均衡的 symmetric 對稱的 symmetric 對稱 symmetric adj 1: having similarity in size, shape, and relative position of corresponding parts [synonym: {symmetrical}, {symmetric}] [ant: {asymmetric}, {asymmetrical}] Symmetric \Sym*met"ric\, a. Symmetrical. [1913 Webster] 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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