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Epsilon delta rule states

  1. May 4, 2009 #1
    The epsilon delta rule states

    [TEX]\epsilon_{ijk}\epsilon_{pqk}=\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp}[/TEX]

    I am constantly using this but get stuck when it is applied.

    For example

    [TEX]\epsilon_{ijk}\epsilon_{pqk}A_{j}B_{l}C_{m}=(\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp})A_{j}B_{l}C_{m}[/TEX]

    This then becomes

    [TEX]A_{j}B_{i}C_{j}-A_{j}B_{j}C_{i}[/TEX]

    Can anybody please explain this result????

    Is it true that

    [TEX]\delta_{ij}a_{i}=a_{j}[/TEX]

    If so does this not apply to the above
     
    Last edited: May 4, 2009
  2. jcsd
  3. May 4, 2009 #2

    DrGreg

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    Science Advisor
    Gold Member

    Re: Epsilon-delta?

    Just replace the word MATH by TEX. You can go back and edit your previous post within 24 hours (I think) of posting it.
     
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