Derivate of geometrical product

[Raparicio]

Dear Friends

I'd like to know if anybody has the solution of the aplication of nabla's operator to geometrical product:

ab=a·b+a^b

And if it's possible to apply a operator like this:

d/dt + d/dx i + d/dy j + d/dz k.

My best reggards.

 

[quasar987]

What is the geometrical product? Mathworld doesn't know.

About "d/dt + d/dx i + d/dy j + d/dz k". You wish to apply this operator to a scalar function? I don't know but the result would be a scalar + a vector. The operation of addition is not defined between those two identities afaik.

 

[Hurkyl]

It sounds a lot like the OP is working with quaternions... as a real vector space, their standard basis vectors are often written 1, i, j, k. The 1 is often suppressed.

It's also true that $a b = a\cdot b \vec{1} + a \times b$, where the first product is ordinary quaternion multiplication.

 

[robphy]

This "geometric product" is from (Hestenes) "Geometric Algebra".
http://planetmath.org/encyclopedia/GeometricAlgebra.html

http://modelingnts.la.asu.edu/
http://faculty.luther.edu/~macdonal/ might have some useful articles

 

[Raparicio]

Thanks! very useful!