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Homework Help: Another gravitation problem

  1. Nov 25, 2011 #1
    I need to find the relation between [tex] E^{2}-B^{2} [/tex] and [tex] F_{\mu\nu} F^{\mu\nu} [/tex]
    Actually, I need to use this relation to determine that the first is a scalar.
    What I can't understand is how these notations match the formal definition:
    If I multiply a matrix by another (same size) I should be receiving another matrix of the same size. Not a scalar...
    But if I use the notations I need to use here:
    [tex] F_{\mu\nu} F^{\mu\nu}\Rightarrow \Sigma_{i=1}^{3} \Sigma_{j=1}^{3} = F_{00}F^{00}+F_{01}F^{01}+...
    [/tex] and that is not the product I expect it to be...
    Could someone explain me how these definitions get along?
    Thank you!
  2. jcsd
  3. Nov 26, 2011 #2
    Anybody...? I am lost in here ...
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