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Divergence of a rank-2 tensor in Einstien summation

  1. Dec 29, 2013 #1
    1. The problem statement, all variables and given/known data
    Hi

    When I want to take the divergence of a rank-2 tensor (matrix), then I have to apply the divergence operator to each column. In other words, I get
    [tex]
    \nabla \cdot M = (d_x M_{xx} + d_y M_{yx} + d_zM_{zx}\,\, ,\,\, d_x M_{xy} + d_y M_{yy} + d_zM_{zy}\,\,,\,\, d_x M_{xz} + d_y M_{yz} + d_zM_{zz})
    [/tex]
    How would I write this vector in Einstein summation? Is it correct that it would be
    [tex]
    \partial_i M_{ij}
    [/tex]
     
  2. jcsd
  3. Dec 29, 2013 #2
    IIRC, yes.

    You have three entries, that distinguished by a new j value, since it appears once, and each entry is a summation over i, since it appears twice.
     
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