Homework Help: Gradient of vector

Visually, what you wrote looks like

[tex]\nabla_{\vec A}[/tex]

The title of the thread and your LaTeX suggests you meant

[tex]\nabla \vec A[/tex]

These are two different things. The first is an operator, the gradient with respect to the components of [itex]\vec A[/itex], rather than the normal gradient which is take with respect to spatial components. The second form is the gradient of a vector. It is a second-order tensor. If [tex]\vec A = \sum_k a_k \hat x_k[/tex],

[tex](\nabla \vec A)_{i,j} = \frac{\partial a_i}{\partial x_j}[/tex]

BTW, it is best not to separate things the way you did in the original post. Here is your original equation as-is:

[tex]\nabla[/tex][tex]\stackrel{\rightarrow}{A}[/tex]

Now look at how this appears when written as a single LaTeX equation:

[tex]\nabla\stackrel{\rightarrow}{A}[/tex]

 

Does this make a matrix using row i and column j for the entries?

 

Yes.

 

Thank you.