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.