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A really easy question on properties of the Levi-Civita tensor and index interchange

  1. Feb 28, 2009 #1
    Does the following identity hold?:

    [tex]
    \epsilon_{ijk} a_j b_k = -\epsilon_{ijk} a_k b_j
    [/tex]
     
  2. jcsd
  3. Feb 28, 2009 #2

    cristo

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    Staff Emeritus
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    Re: A really easy question on properties of the Levi-Civita tensor and index intercha

    Yes.
     
  4. Feb 28, 2009 #3
    Re: A really easy question on properties of the Levi-Civita tensor and index intercha

    The answer is yes; clearly we have:
    [tex]
    \epsilon_{ijk} a_j b_k = -\epsilon_{ikj} a_j b_k
    [/tex]

    from which we can obtain your identity by relabeling the dummy indices j and k.
     
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