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!

How to evaluate gradient of a vector? or del operator times a vector

  1. Sep 15, 2010 #1
    How will i find the gradient of a vector?
    i know that gradient is only for scalar to produce a vector? i am confuse since del operator is a vector how will i find the gradient of a vector.
    How can i multiply a del operator and vector
  2. jcsd
  3. Sep 16, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Usually, an expression like [tex]\nabla \vec v[/tex] doesn't make sense.
    You might mean [tex]\nabla \cdot \vec v[/tex] instead, which (as a dot product) produces a scalar, or [tex]\nabla \times \vec v[/tex] which (as a cross product) produces a vector.
    Only in specific contexts, the expression [tex]\nabla \vec v[/tex] may have a meaning, for example in Clifford algebras or in multi-variable analysis as a shorthand for a matrix like
    [tex]A_{ij} = \frac{\partial \vec v_i}{\partial x_j}[/tex]
    (although I must admit I've never seen it used like that).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook