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symmetricmore about symmetric

symmetric

 

  3  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Symmetric  \Sym*met"ric\,  a. 
  Symmetrical. 
 
  From  WordNet  r  1.6  [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  (13  Mar  01)  [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)




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