On Wed, 7 Sep 2011, William Tanksley, Jr wrote: > Nothing. > > On a tangentially related subject... Has anyone done any work with > Clifford or spacetime algebras in J? It would seem to be a natural > fit. > > This page http://www.valdostamuseum.org/hamsmith/clfpq2.html > speculates that the algebraic structure of spacetime appears to be a > 2x2 matrix of quaternions -- how good is J at quaternion math? It also > mentions that another possibility (which it doesn't consider a good > fit, although it's nominally possible) would be the space of 4x4 > matrices of reals (which I know J can do, and therefore might be a > better start). > > -Wm > There is a formulation of Clifford algebra called "Geometric Algebra". The cross product shouldn't really be a vector at all, but a 2-d surface in the plane of the two vectors. This clears up a lot of stuff (axial vs polar vectors, etc.). This is worked out in great detail as applied to various areas of physics. See
A. Lasenby & C. Doran, Geometric Algebra for Physicists (Cambridge U. Press, Cambridge 2002). > On Wed, Sep 7, 2011 at 7:49 AM, Raul Miller <[email protected]> wrote: >> On Wed, Sep 7, 2011 at 10:03 AM, Devon McCormick <[email protected]> wrote: >>> Doesn't this restrict it to three dimensions? >> >> What does cross product mean in two dimensions? >> >> -- >> Raul >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
