1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gradient of vector

  1. May 29, 2008 #1

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

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    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:


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

    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

    User Avatar
    Staff Emeritus
    Science Advisor

  6. Sep 22, 2009 #5
    Thank you.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Gradient of vector
  1. Gradient question (Replies: 6)

  2. Deformation gradient (Replies: 0)

  3. Gradient of (1/r) (Replies: 5)