Archive for July, 2006

The cross product

Posted in Physics 4 years, 1 month ago

I don’t like it so much.

The cross product is defined as A \times B = \epsilon_{ijk} A^j B^k . It’s generally used to find a vector in R^3 that is orthogonal to two other vectors.

Firstly, the cross product does not generalize cleanly to dimensions greater than three. There are a lot of cool numerical tricks used to solve differential equations and it’d be nice if we could make use of them to solve more complicated problems. Fortunately, for the orthogonalization problem, there are far better schemes.

Secondly, the vector (0,0,0) is really a point and represents a singularity in the system. The cross product of a vector with this point will map onto another point (which is again (0,0,0)). I’m not really sure whether this should be handled as a special case in your numerical code.

That is all.

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