Nabla operator to geometric 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

(inner and outer product)

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

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

and the rules to operate.

My best reggards.

 

[Raparicio]

Triple geometrical product?

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
(inner and outer product)
And if it's possible to apply a operator like this:
d/dt + d/dx i + d/dy j + d/dz k.
and the rules to operate.
My best reggards.

Another question about this is:

geometrical produt is

ab=a·b+a^b

and geometrical product of abc?

 

[M98Ranger]

Hello,

The application of nabla's operator to the geometric product is a useful tool in geometric algebra. The result of applying nabla to a geometric product is a vector, which can be expressed as the sum of an inner product and an outer product. This is known as the fundamental theorem of geometric calculus.

As for your second question, it is indeed possible to apply operators such as d/dt, d/dx, d/dy, and d/dz to geometric products. This allows for the manipulation of vectors and multivectors in a similar manner to traditional calculus. The rules for operating with these operators can be found in many textbooks and online resources on geometric algebra.

I hope this helps answer your questions. Best regards.