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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
Are we having fun, yet?
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