- #1

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when a gradient operater act on a vector,what is it stand for ?

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- Thread starter enricfemi
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- #1

- 191

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when a gradient operater act on a vector,what is it stand for ?

- #2

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when a gradient operater act on a vector,what is it stand for ?

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]

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- #3

- #4

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Yes.

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Thank you.

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