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Homework Help: Tensors (2)

  1. Mar 30, 2009 #1
    [itex]T_{ijk}[/itex] is an array with 27 components which is not known to represent a tensor. If for every second rank tensor, [itex]R_{ij}[/itex], the quantity [itex]v_i=T_{ijk}R_{jk}[/itex] is always a vector, show that [itex]T_{ijk}[/itex] is a third rank tensor.

    I've managed the bit above. Just stuck on the next part:

    If [itex]R_{ij}[/itex] is any symmetric tensor and [itex]v_i[/itex] is again always a vector, what can be said about the transformation properties of [itex]T_{ijk}[/itex] and [itex]T_{ijk}+T_{ikj}[/itex]???
  2. jcsd
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