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Homework Help: Kroenecker delta δ question

  1. Oct 8, 2012 #1
    1. The problem statement, all variables and given/known data
    kroenecker delta has one upper and one lower index. except from uppper index and lower index,we have 2 slots for the upper index and 2 slots for the lower index(for a 2 index tensor).
    Why krenecker delta left or right slot index position doesnt matters?
    Also why 2 two index tensors may not be equal because of the peculiarity of left and right slot index position?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 9, 2012 #2
    That's just because of the definition. Tensors that behave like this are called symmetric.

    I don't understand what this question means.
     
  4. Oct 9, 2012 #3

    dextercioby

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    Science Advisor
    Homework Helper

    Because of the general definition of a tensor as a multilinear mapping, the order in which the vector spaces and their duals are chosen really matters, especially when the bundle of tensors is defined for a metric manifold (as is the case in relativity).

    You will study electrodynamics and discover that the mixed components of the field tensor are all different, that is

    [tex] F_{\mu}^{~~\nu} \neq F^{\nu}_{~~\mu} [/tex]

    for arbitrary index values.
     
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