# Tensors (2)

1. Mar 30, 2009

### latentcorpse

$T_{ijk}$ is an array with 27 components which is not known to represent a tensor. If for every second rank tensor, $R_{ij}$, the quantity $v_i=T_{ijk}R_{jk}$ is always a vector, show that $T_{ijk}$ is a third rank tensor.

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

If $R_{ij}$ is any symmetric tensor and $v_i$ is again always a vector, what can be said about the transformation properties of $T_{ijk}$ and $T_{ijk}+T_{ikj}$???