Derivate of geometrical product

In summary, the conversation is about the application of nabla's operator to the geometrical product and the possibility of applying a similar operator. It is mentioned that this operator may be used with quaternions and it is also referred to as the "geometric product" from "Geometric Algebra." Links to further resources are provided.
  • #1
Raparicio
115
0
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.
 
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  • #2
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.
 
  • #3
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. :smile:

It's also true that [itex]a b = a\cdot b \vec{1} + a \times b[/itex], where the first product is ordinary quaternion multiplication.
 
  • #5
Thanks! very useful!
 

1. What is a derivative of geometrical product?

A derivative of geometrical product is a mathematical concept that represents the rate of change of a product between two geometric figures. It is calculated using the principles of calculus, specifically the derivative function.

2. How is the derivative of geometrical product calculated?

The derivative of geometrical product is calculated using the chain rule of differentiation. This involves taking the derivative of each individual component of the product and then multiplying them together.

3. What is the significance of the derivative of geometrical product?

The derivative of geometrical product is important in understanding the relationship between two geometric figures, as it gives insight into how they change in relation to each other. It is also useful in solving optimization problems in geometry.

4. Can the derivative of geometrical product be negative?

Yes, the derivative of geometrical product can be negative if the rate of change between the two geometric figures is negative. This indicates that the product is decreasing as the figures change.

5. In what fields is the derivative of geometrical product commonly used?

The derivative of geometrical product is commonly used in fields such as engineering, physics, and computer graphics. It is also applicable in geometric modeling and computer-aided design.

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