Re: Dot product confusion

*To*: mathgroup at smc.vnet.net*Subject*: [mg109956] Re: Dot product confusion*From*: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>*Date*: Wed, 26 May 2010 07:09:39 -0400 (EDT)

Hi Steve >From the Mathematica documentation for Dot: "The dimensions of the result are those of the input with the common dimension collapsed:" There is then an example where an object with Dimensions "{2, 3, 4}" Dotted with an object with Dimensions "{4,5,2}" gives an object with dimensions "{2,3,5,2}". ptsa = {{x1, y1, z1}, {x2, y2, z2}, {x3, y3, z3}} Dimensions @ ptsa The matrix ptsa has dimensions 3*3. Dimensions @ {aa, bb, cc} {aa, bb, cc} is a list with dimension 3: The product {aa, bb, cc}.ptsa is thus the dot product of a "3" and a "3*3" giving a result with dimension 3: {aa, bb, cc}.ptsa (* expression 1 *) Dimensions @ % On the other hand, ptsa.{aa, bb, cc} is the dot product of a " 3*3" and a "3" giving (another) result with dimension 3: ptsa.{aa, bb, cc} (* expression 2 *) Dimensions @ % Note that: Dimensions @ Transpose[{{aa, bb, cc}} ] Transpose[{{aa, bb, cc}} ] is a column vector with dimensions 3*1. So, ptsa.Transpose[{{aa, bb, cc}} ] is the dot product of a " 3*3" and a "3*1" giving a result with dimension 3*1: ptsa.Transpose[{{aa, bb, cc}} ] (* expression 3 *) Dimensions @ % Barrie >>> On 25/05/2010 at 8:32 pm, in message <201005251032.GAA20697 at smc.vnet.net>, "S. B. Gray" <stevebg at ROADRUNNER.COM> wrote: > 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