Symmetric

3 definitions found

From The Collaborative International Dictionary of English v.0.48 [gcide]:

  Symmetric \Sym*met"ric\, a.
     Symmetrical.
     [1913 Webster]

From WordNet (r) 2.0 [wn]:



  symmetric
       adj : having similarity in size, shape, and relative position of
             corresponding parts [syn: {symmetrical}] [ant: {asymmetrical}]

From The Free On-line Dictionary of Computing (27 SEP 03) [foldoc]:

  symmetric
       
           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)