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Re: Dot product confusion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109957] Re: Dot product confusion
  • From: dh <dh at metrohm.com>
  • Date: Wed, 26 May 2010 07:09:50 -0400 (EDT)
  • References: <htg90l$k7h$1@smc.vnet.net>

Hi Steve,
the "." product is defined as:
Sum[x1[[..,i]] x2[[i,..]],{i,1,n}]
that is the last index of x1 is contracted with the first index of x2.
 From this it is clear that commutivity only exists if x1 and x2 are 
cheers, Daniel

Am 25.05.2010 12:32, schrieb S. B. Gray:
> Given
>
> ptsa = {{x1, y1, z1}, {x2, y2, z2}, {x3, y3, z3}};
>
> I  thought the following expressions would be identical:
>
> {aa, bb, cc}.ptsa  (* expression 1 *)
> ptsa.{aa, bb, cc}  (* expression 2 *)
>
> but they are not. They evaluate respectively as:
>
> {aa x1 + bb x2 + cc x3, aa y1 + bb y2 + cc y3,
> aa z1 + bb z2 + cc z3}
>
> {aa x1 + bb y1 + cc z1, aa x2 + bb y2 + cc z2,
>    aa x3 + bb y3 + cc z3}
>
> Since ptsa is itself three xyz coordinates, the expressions might be
> ambiguous, but I assumed the dot product would always commute. Should
> there be a warning?
>
> The first result is the one I want.
>
> Steve Gray
>


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