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Dot product between tensors

  1. Apr 11, 2012 #1
    Hi there. I have this problem, which says: In the cartesian system the tensor T, twice covariant has as components the elements of the matrix:
    [tex]\begin{bmatrix}{1}&{0}&{2}\\{3}&{4}&{1}\\{1}&{3}&{4}\end{bmatrix}[/tex]

    If [tex]A=e_1+2e_2+3e_3[/tex] find the inner product between both tensors. Indicate the type and order of the resultant tensor.

    Well, I don't know how to do this. Which type of tensor is A? I think that could help.
    The inner product is defined for tensors of different kinds as:
    [tex]S=u^iv_i[/tex]

    The supraindex indicates contravariance and the subindex covariance.
     
  2. jcsd
  3. Apr 11, 2012 #2

    tiny-tim

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    Hi Telemachus! :smile:

    I think they're saying that A is first-order contravariant, so T.A will be TijAj :wink:

    (btw, not what i'd call a dot product :frown:)
     
  4. Apr 11, 2012 #3
    Why not?

    Thank you Tim :)
     
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