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MathGroup Archive 1998

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Re: Re: Vectors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13977] Re: [mg13953] Re: Vectors
  • From: Carl Woll <carlw at fermi.phys.washington.edu>
  • Date: Sat, 12 Sep 1998 16:59:04 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

On Fri, 11 Sep 1998, AES wrote:

Hi,

I think you are being unfair to Mathematica here.

> 
> You're running into the always bewildering notational inconsistencies of
> Mathematica.  Consider
> 
>    A = ={{a,b,c}}
>    B = {{d},{e},{f}}
> 
> (note bracketing).  Are these vectors?  Well, they can be dotted, as in
> 
>    A . B
> 
> and
> 
>    B . A
> 

Actually, A and B here are matrices, not vectors, and the dot product
corresponds to matrix multiplication. That is, A.B produces the 1 x 1
matrix 

(a d + b e + c f)

and B.A produces the 3 x 3 matrix

a d   b d   c d
a e   b e   c e
a f   b f   c f

> and you'll get the right answer in each case.  So, if they can be
> "dotted", they ought to be "cross-able" as well, right? So try
> 
>    Cross[A,B]
>    Cross[B,A]
>    Cross[A,A]
>    Cross[B,B]
> 
> and find that _none_ of these work.  

Since A and B are matrices and not vectors, Cross doesn't work.

> Now, page 115 of the Bible says
> that Cross[a,b] can also be input as a * b, so try instead
> 
>    A * B
>    B * A
>    A * A
>    B * B
> 
> and get three or four different answers; some of these work, some don't.
> 
> Just don't expect consistency!
> 

The Book says you can input Cross[a,b] as a \[Cross] b, where \[Cross]
comes out looking like a small, bold x. You can't input Cross[a,b] with
a*b, since * is simply ordinary multiplication.

So, I don't think Mathematica is being obscure or inconsistent here.

Carl Woll
Dept of Physics
U of Washington



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