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Antisymmetric gradient matrix?

  1. Sep 11, 2014 #1
    Does this operator (in 3D):

    [tex]ε_{ijk}∇_k = \begin{pmatrix}
    0 & \frac{\partial}{\partial z} & -\frac{\partial}{\partial y}\\
    -\frac{\partial}{\partial z} & 0 & \frac{\partial}{\partial x}\\
    \frac{\partial}{\partial y} & -\frac{\partial}{\partial x} & 0

    have a formal name and a more compact symbolic representation?
    Last edited: Sep 11, 2014
  2. jcsd
  3. Sep 12, 2014 #2


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    Science Advisor
    Gold Member

    That gives you the curl in 3-D.

    It gives you an analogue of the curl in other dimensions. I don't know how much more compact than ##\epsilon_{ijk}\nabla_k## you wanted, but I am not aware of any more compact forms.
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