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Index Notation and Kronecker Delta

  1. Jul 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Simplify the following expressions involving the Kronecker delta in N dimensions. Where possible, write the final result without indices.

    [itex]C_{ns}\delta_{rn}[/itex]

    2. Relevant equations



    3. The attempt at a solution

    I know Kronecker delta is symmetric but that doesn't seem to help. Is this undefined?
     
  2. jcsd
  3. Jul 17, 2011 #2

    Pengwuino

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    Hmm this sounds too simple, is there something special about C?
     
  4. Jul 17, 2011 #3
    There's nothing special about C, the exercise is to just get us used to index notation and what it means I think but I'm struggling a bit. The next question is:

    [tex]A_{ij}B_{nk}C_{rs}\delta_{jr}\delta_{sn}\delta_{ik}[/tex]

    but I can't do that until I figure out how to work with delta above...
     
  5. Jul 17, 2011 #4

    Pengwuino

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    Well what's the definition of the Kronecker delta?
     
  6. Jul 17, 2011 #5
    It's the identity matrix, but [tex]\delta_{rn}[/tex] could be either 0 or 1 depending on if r=n or r=/=n...

    EDIT r=/=n
     
    Last edited: Jul 17, 2011
  7. Jul 17, 2011 #6

    Pengwuino

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    So if you have something like [itex]C_{ns}\delta_{rn}[/itex], that means this term is only non-zero when r=n so you can simplify the expression as [itex]C_{rs}[/itex]
     
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