- To: mathgroup at smc.vnet.net
- Subject: [mg30674] Engineer's Stunt
- From: bruce.detterich at ieee.org (Bruce Detterich)
- Date: Sat, 8 Sep 2001 02:22:14 -0400 (EDT)
- References: <email@example.com>
- Sender: owner-wri-mathgroup at wolfram.com
The prior descriptions were a bit too complicated for my poor simple mind. Here's a little trick I use to remember how to generate Cross product and the 3-dimensional special case, "Curl". To generate the cross product of two vectors, e.g. A X B, assuming the conventional unit vectors: i, j and k, simply expand by minors the matrix whose first row elements are: i, j and k; second row elements are: Ax, Ay, Az; and third row elements are: Bx, By, and Bz. The Curl of B can be created by simply replacing the vector A in the above example by the row vector of partial derivative operators: d/dx, d/dy and d/dz. I use the term 'expand my minors' to mean taking each element of the first row, signed per usual convention, and multiplying it by the result of expansion of its related 2X2 minor. Again, don't forget the sign reversal of the j element due to its 'odd' sum-of-indices. I assume that Mathematica uses some vastly more sophisticated approach to the problem, but I know the above is pretty much bullet proof.