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Homework Help: The Kronecker delta

  1. Sep 17, 2003 #1
    i need help....:frown:
    prove SUM(k) [E(ijk)E(lmk)]= d(il)d(jm) - d(im)d(jl)
    where "d" is Kronecker delta symbol and "E" is permutation symbol or
    Levi-Civita density
     
    Last edited by a moderator: Feb 6, 2013
  2. jcsd
  3. Sep 18, 2003 #2

    HallsofIvy

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    Science Advisor

    A clarification: the Kronecker delta, d(ij), is 1 if i= j, 0 otherwise.

    The Levi-Civita permutation symbol, E(ijk) {real notation is "epsilon"), is 1 if ijk is an even permutation of 123, -1 if ijk is an odd permutation of 123, and 0 otherwise. While d(ij) is defined for all dimensions, E(ijk) implies that i, j, and k can only be 1, 2 ,3. For higher "dimensions" we would need more indices.

    SUM(k) [E(ijk)E(lmk)]= E(ij1)E(lm1)+ E(ij2)E(lm2)+E(ij3)E(lm3)
     
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