# Outer differentiation?

1. Feb 19, 2004

### Creator

"outer" differentiation?

Since I didn't get a response on the "Diff. Eqns." thread, I put it here.

Can someone give me a clear explaination of what is meant by "outer" differentiation.

As for example, when we differentiate the vector potential, dA/dx, in order to arrive at the magnetic field, B, why would this be called an 'outer' differentiation??

[?]

2. Feb 19, 2004

### turin

Re: "outer" differentiation?

Probably because d/dx is not exactly what you do. You take the cross product of the gradient operator with the vector potential to get the magnetic field. The cross product is sometimes called/related to the outer product, but that's tensor jargon with which I am unfamiliar.

3. Feb 20, 2004

### Creator

Re: Re: "outer" differentiation?

Thanks for the response, Turin;

and thanks for the correction. Oc course, you are accurate in saying it is the cross product of the gradient.
I guess then if someone says "dA/dt is the outer differentiation" I should interpret that to mean they are simply referring to it as being a cross product.??

4. Feb 20, 2004

### turin

Re: Re: Re: "outer" differentiation?

I would ask them what they mean. I wouldn't know how to make sense of that.