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Jacobean matrix

  1. Aug 31, 2012 #1
    I'm not sure if this belongs in physics or here. Consider the transformation of a vector from one coordinate system to the other. I can write:

    Vn = (∂yn/∂xm)Vm - contravariant form

    Vn = (∂xm/∂yn)Vm - covariant form

    In each case are the partials equivalent to the Jacobean matrices? Also, what about the case of a tensor

    Tmn = (∂xr/∂ym)(∂xs/∂yn)Trs

    Is the transformation just the product of 2 Jacobeans?
  2. jcsd
  3. Sep 1, 2012 #2


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    Yes, the Jacobian is used to describe coordinate changes. Is that what you

    were asking?
  4. Sep 1, 2012 #3
    Yes. I wasn't quite sure if there were any implications associated with covariant versus contravariant vectors in differential geometry. Also, in the case of a tensor, I wasn't sure if the transformation was the product of the Jacobean with it's inverse or transpose.
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