Question from someone just starting to study tensors (sorry if it's silly):
So I understand (maybe?) that tensors are basically about coordinate transformations (and things that are invariant under said transformations), and that in writing out a tensor, we use notation that represents functions that perform the coordinate transformations.
But when I see a tensor of, say, rank 3 or 4 written out, it looks like we're jumping from one coordinate system to another to another, before we arrive from the original coordinate system to the final one. If you're only really starting at one coordinate system, and ending at another, why can't you treat each tensor as just a single coordinate transformation, i.e. a function that takes you directly from the original coordinate system to the final one?