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Math Help - Relationship between Kronecker Delta and the Alternating Tensor

  1. #1
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    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?

    Thanks in Advanced,

    James Elmore

    P.S.
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  2. #2
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    Are you asking how the relationship was dreamed up in the first place? Or are you asking how do you prove the relationship?
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  3. #3
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    I'm more interested in the proof of the relationship
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  5. #5
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    Quote Originally Posted by Ackbeet View Post
    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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  6. #6
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