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Matrix Representation of Tensors?

  1. Aug 20, 2008 #1
    How would you represent tensors as matrices? I've searched all over, and my book on GR (Wald) only has one example where he makes a matrice from a tensor, and I still don't understand the process.
     
  2. jcsd
  3. Aug 20, 2008 #2

    George Jones

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    A tensor is a muti-linear mappring. A rank 2 tensor can be turned into a matrix by letting it operate on a basis or dual basis. See,

    https://www.physicsforums.com/showthread.php?p=874061&#post874061

    but this might not have enough detail.
     
  4. Aug 20, 2008 #3

    how often are rank-2 tensors used in GR, by chance?
     
  5. Aug 20, 2008 #4

    George Jones

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    Quite often; the metric tensor, the stress-energy tensor, the Einstein tensor, and the Ricci tensor all examples of rank 2 tensors.

    Introducing a basis turns (the components of):

    a rank 1 tensor into a column or row of values;

    a rank 2 matrix into a square matrix of values;

    a rank 3 tensor into a cube with values in each subcubes (think rubik's cube).
     
  6. Aug 20, 2008 #5

    okay, that's what I thought... thanks a lot for your help!
     
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