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The Kronecker delta 
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#1
Sep1703, 11:00 AM

P: 152

i need help....
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 LeviCivita density 


#2
Sep1803, 05:28 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,552

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