1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    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)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: The Kronecker delta
  1. Delta epsilon (Replies: 4)

  2. D and delta (Replies: 3)

  3. Delta Vee (Replies: 1)