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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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