Re: Dot product confusion

*To*: mathgroup at smc.vnet.net*Subject*: [mg109964] Re: Dot product confusion*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Wed, 26 May 2010 07:11:07 -0400 (EDT)

On 5/25/10 at 6:32 AM, stevebg at ROADRUNNER.COM (S. B. Gray) 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. >Since ptsa is itself three xyz coordinates, the expressions might be >ambiguous, but I assumed the dot product would always commute. The dot product of two *vectors* commutes. But you are multiplying a matrix by a vector which does not commute in general >Should there be a warning? No. Until Mathematica is run on a machine with artificial intelligence and has the capability of reading minds, there isn't any way for Mathematica to determine the user expected a result different from the correct mathematical result.