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

Abir Sarkar

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 ?

dextercioby

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

dextercioby Blog Entries: 9 Recognitions: Homework Help Science Advisor	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.