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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

    CompuChip

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    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).
     
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