Since affine transforms involve a matrix, if the transform matrix is a tensor, it would be of rank two. But, the real question is whether or not a change of basis, or transformation of the underlying space, effects the resultant vector linearly. Is that the correct argument? If the previous is true, I'd argue the affine transformation matrices are tensors since affine transformations are also linear in nature.
So are affine transformation matrices tensors of rank two? Similar to the rank two stress tensor composed of matrices.
This question is motivated by a desire to find intuitive examples of tensors, since I already know what an IFS is, this would make things very easy.
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