Vector multiplication??

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Vector multiplication??*From*: "Katherine (Williams) Derbyshire" <kewms at kew.com>*Date*: Wed, 02 Dec 1992 22:47:19 EST

On Wed, 2 Dec 92 14:14:50 -0500, "Paul N. Schatz" <pns at fermi.clas.virginia.EDU wrote: On Nov 29, 15:48, "Katherine (Williams) Derbyshire" wrote: Subject: Vector multiplication?? I have an arbitrary vector A = Array[a,3] = {a[1], a[2], a[3]} The dot product of this vector with itself, is evaluated correctly by Mathematica: a[1]^2 + a[2]^2 + a[3]^2 The 'ordinary' product of this vector with itself, A^2, should be equivalent to the dot product. It is, in fact, conventional in mechanical engineering to interpret A^2 as the square of the magnitude of A, (i. e. as a dot product). My linear algebra text doesn't offer any definition for this expression at all. Unfortunately, Mathematica (2.0 for Windows) interprets A^2 as {a[1]^2, a[2]^2, a[3]^2} which isn't the same at all. I would like to point out that this is NOT a wrong answer. The product in question is called the Hadamard product. It in fact is EXCEEDINGLY useful in many Mathematica applications. My apologies. I guess this is a case of not enough symbols available, so they all get overloaded. Sigh... Just out of curiousity, what sorts of applications use the Hadamard product? Katherine -- Katherine (Williams) Derbyshire kewms at kew.com Are we having fun, yet?