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Help with tensor homework

  1. Apr 26, 2009 #1
    if [itex]\epsilon_{ijk} P_{kj}=0[/itex] how do we show [itex]P_{ij}=P_{ji}[/itex]?
     
  2. jcsd
  3. Apr 26, 2009 #2

    dx

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    Re: tensors

    Expand out the LHS for each i.
     
  4. Apr 26, 2009 #3
    Re: tensors

    do you mean just substitute in numbers and see what happens because that works - i was just wondering if i could do it without explicitly using numbers (i.e. all of it in index notation).
     
  5. Apr 26, 2009 #4

    dx

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    Re: tensors

    For i = j, clearly Aij = Aji, so you only need to check the cases in which i ≠ j.

    For example, setting i = 1 in εijkAkj = 0, you get ε123A32 + ε132A23 = A32 - A23 = 0 ⇒ A32 = A23.

    You just need to do the same with i = 2 and i = 3.
     
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