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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