Dot product confusion
in [Mathematica]
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From: S. B. Gray on 25 May 2010 06:32 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
From: Alois Steindl on 26 May 2010 07:06 Hello, your assumptions seem to be wrong. The dot product in Mathematica isn't just "the inner product, but the matrix product, in your case ptsa*v or v*ptsa. In the first case v is considered as column vector, in the second one as row vector. Matrix products are rarely abelian. Alois -- Alois Steindl, Tel.: +43 (1) 58801 / 32558 Inst. for Mechanics and Mechatronics Fax.: +43 (1) 58801 / 32598 Vienna University of Technology, A-1040 Wiedner Hauptstr. 8-10
From: S. B. Gray on 26 May 2010 07:08 On 5/25/2010 3:32 AM, 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. 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 > Thanks to all who answered my question. I temporarily forgot about matrix - vector multiplication.
From: Mark Adler on 26 May 2010 07:08 On 2010-05-25 03:32:53 -0700, S. B. Gray said: > ptsa = {{x1, y1, z1}, {x2, y2, z2}, {x3, y3, z3}}; The dot product of two vectors commutes, but your ptsa is a matrix. In general matrix multiplication does not commute. > {aa, bb, cc}.ptsa (* expression 1 *) > ptsa.{aa, bb, cc} (* expression 2 *) Mathematica treats ptsa as a column vector (1x3) in expression 1, and as a row vector (3x1) in expression 2. Mark
From: Christopher Arthur on 26 May 2010 07:08
try putting the vector in braces like this {{a},{b},{c}} for a column vector into a row vector S. B. Gray a =E9crit : > 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 > > > |