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Matrix Formalism of Differential Geometry

  1. Nov 20, 2009 #1
    I would like to explore writing differential geometry in matrix format and was wondering if any of the experts here knows a good resource for that? I have tried Google and can't find anything definitive.

    Thanks in advance!
     
  2. jcsd
  3. Nov 21, 2009 #2

    HallsofIvy

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    Are you talking about representing tensors as matrices?
     
  4. Nov 21, 2009 #3
    Yes. The metric tensor would become a 4x4 hermitian matrix.
     
  5. Nov 22, 2009 #4

    haushofer

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    Well, symmetric 2-tensors are represented by symmetric matrices, like the metric. Antisymmetric 2-tensors are represented by antisymmetric matrices, like the Maxwelltensor. Are there any magical things going on here?

    The matrixform of pushforwards and pullbacks also are quite frequently noted in texts. I must say that I can't think of any subtleties, but maybe this topic,

    https://www.physicsforums.com/showthread.php?t=353536

    helps a little :)
     
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