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How to derive Relation between Levi-civita Density and Kronecker's Delta?

  1. Aug 6, 2011 #1
    The Relation between Levi-Civita Density and Kroneckers Delta as follows



    [itex]\sum^{3}_{k=1} \epsilon_{mnk} \epsilon_{ijk} = \delta_{mi} \delta_{nj} - \delta_{mj} \delta_{ni}[/itex]​




    Logically we can satisfy both sides of the expression but Can anyone tell me how to derive this analytically ?
     
  2. jcsd
  3. Aug 6, 2011 #2

    dextercioby

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    I don't think you can purely derive it, just consider that the RHS must be a-symmetric in m,n and i,j, so it must be an antisymmetrized product of deltas.
     
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