>>12525709Transformations yet but im not so sure they are arbitrary. Perhaps only some transformations are allowed.
The inspiration behind this is physics, there are physical objects that can be called tensors and they look different in different coordinate systems but they represent the same physical object. Rotations and reescaling are typical in R3 but in relativistic physics we want to ask ourselves things like how does the electromagnetic field lools like on different inertial frames. Each frame is associated with a coordinate transformation, its like a rotation but in R4, and it changes how the EM field looks like, but the transformed field still looks like it fits the laws if physics, basically it has the same equations in the transformed variables. In R3 is much simpler, physics does not change if you do a handstand and say gravity is now pushing up instead of pulling down, you just changed the height coordinate from Z->-Z.
Each text on tensors i have seen says that tensors transform according to a "transformation law" which is very tautological. I dont know if that implies any transformation law or SOME transformation that is somehow compatible with the tensors.
Tensors are defined on specific manifolds, like R3 or Minkowsky space, i dont know if the allowed transformations are associated with these manifolds or if it could be literally any transformation.
