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Vector multiplication??

  • To: mathgroup at
  • Subject: Vector multiplication??
  • From: "Katherine (Williams) Derbyshire" <kewms at>
  • Date: Sun, 29 Nov 1992 15:48:41 EST

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
   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.  

What's going on here?  I know I could fix this by writing a
transformation rule, but it would be nice if Mathematica didn't give
wrong answers in the first place.
Katherine (Williams) Derbyshire
kewms at

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