I have two rank-3 tensors, let's call them $T_{1}$ and $T_{2}$. Each is a 3x3x3 tensor, representing voxels in an image. I'd like to determine if $T_{1}$ and $T_{2}$ are related by a rotation / reflection.
For matrices (rank-2 tensors?), I'd assume $M_{1}$ and $M_{2}$ are related by :
$M_{1} = R M_{2}$
Rearrange:
$M_{1} M^{-1}_{2} = R$
Since $M_{1}$ and $M_{2}$ are known and assuming $M_{2}$ is invertible, we can compute $R$. Then we can test if the relation
det$(R) \stackrel{?}{=} \pm 1$
is true. If it is true, then $R$ must be a rotation matrix.
QUESTION:
Is there an equivalent relation for rank-3 tensors?