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Outer product of two one forms.

  1. Nov 13, 2004 #1
    Given two one forms f = (1,1,0,0,) and g=(-1,0,1,0): what are the components of f(x)g ... would appreciate any help.
     
  2. jcsd
  3. Nov 13, 2004 #2
    Outer Product of two One Forms

    Given two one forms f = (1,1,0,0) and g = (-1,0,1,0):
    What would be the Components of f(outer product)g be?
    would appreciate any help.
     
  4. Nov 14, 2004 #3

    pervect

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    I'm not quite sure if the "outer product" is the wedge product or the tensor product. Wikipedia seems to think it's the former. See

    This Link

    The wedge product of u ^ v is

    u (tensor) v - v (tensor) u

    The intent here is to anti-symmetrize the tensor product, The formula above works as written only for rank 1 tensors (but that's what you have).

    The tensor product p = u (tensor) v in component notation for rank 1 tensors is:

    pij = uivj

    Thus (1,2,3) (tensor) (4,5,6) is the second rank tensor (you can think of it as an array)

    1*4 ,1*5, 1*6
    2*4, 2*5, 2*6
    3*4, 3*5, 3*6

    Hope this helps
     
  5. Nov 16, 2004 #4
     
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