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Gradient of vector

  1. May 29, 2008 #1
    [tex]\nabla[/tex][tex]\stackrel{\rightarrow}{A}[/tex]

    when a gradient operater act on a vector,what is it stand for ?
     
  2. jcsd
  3. May 29, 2008 #2

    D H

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    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]
     
    Last edited: May 29, 2008
  4. Sep 22, 2009 #3
    Does this make a matrix using row i and column j for the entries?
     
  5. Sep 22, 2009 #4

    D H

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    Yes.
     
  6. Sep 22, 2009 #5
    Thank you.
     
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