# Thread: Relationship between Kronecker Delta and the Alternating Tensor

1. ## Relationship between Kronecker Delta and the Alternating Tensor

In my Vector Calculus class the book discusses the relationship between Kronecker Delta ( $\delta_{ij}$) and the alternating tensor ( $\epsilon_{ijk}$) as the following:

$\epsilon_{ijk}\epsilon_{klm} = \delta_{il}\delta_{jm} - \delta_{im}\delta_{jl}$

The book gives a lengthy explanation of why these two expressions are equivalent, but gives no insight as to how this relation was derived.

Can anyone give any insight into the derivation of this equation?

James Elmore

P.S.
Is this the right board for this topic?

2. Are you asking how the relationship was dreamed up in the first place? Or are you asking how do you prove the relationship?

3. I'm more interested in the proof of the relationship

4. Originally Posted by Ackbeet
That link leaves me in a similar place.

Where did they get the first equation of:

$\epsilon_{ijk}\epsilon_{lmn} = \mbox{det}\left(\begin{array}{ccc}\delta_{il}&\del ta_{im}&\delta_{in}\\\delta_{jl}&\delta_{jm}&\delt a_{jn}\\\delta_{kl}&\delta_{km}&\delta_{kn}\end{ar ray}\right)$

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### relation b/w alternating tensor and kronecker tensor

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