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MathGroup Archive 1992

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Vector multiplication??

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Vector multiplication??
  • From: "Katherine (Williams) Derbyshire" <kewms at kew.com>
  • Date: Wed, 02 Dec 1992 22:47:19 EST

  On Wed, 2 Dec 92 14:14:50 -0500, "Paul N. Schatz" <pns at fermi.clas.virginia.EDU  wrote:
    On Nov 29, 15:48, "Katherine (Williams) Derbyshire" wrote:
      Subject: Vector multiplication??
      I have an arbitrary vector
         A = Array[a,3] = {a[1], a[2], a[3]}
      
      The dot product of this vector with itself, is evaluated correctly by
      Mathematica:
         a[1]^2 + a[2]^2 + a[3]^2
      
      The 'ordinary' product of this vector with itself, A^2, should be
      equivalent to the dot product.  It is, in fact, conventional in
      mechanical engineering to interpret A^2 as the square of the magnitude
      of A, (i. e.  as a dot product).  My linear algebra text doesn't offer
      any definition for this expression at all. Unfortunately, Mathematica
      (2.0 for Windows) interprets A^2 as
         {a[1]^2, a[2]^2, a[3]^2}
      which isn't the same at all.  
  
  I would like to point out that this is NOT a wrong
  answer.  The product in question is called the Hadamard product.
  It in fact is EXCEEDINGLY useful in many Mathematica
  applications.
  
My apologies.  I guess this is a case of not enough symbols
available, so they all get overloaded.  Sigh...
  
Just out of curiousity, what sorts of applications use the Hadamard
product?  

Katherine
-- 
Katherine (Williams) Derbyshire
kewms at kew.com

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