Original sentence: There are infinitely many possible reference frames because there are many nonequivalent bases for a vector space, even after rescaling.Whereas for scalar-valued functions there is only a single possible reference frame up to rescaling (that is, up to a choice of units), to take the derivative of a vector-valued function requires the choice of a reference frame (at least when a fixed Cartesian coordinate system is not implied as such)
Edited sentence: Whereas for scalar-valued functions there is only a single possible reference frame, to take the derivative of a vector-valued function requires the choice of a reference frame (at least when a fixed Cartesian coordinate system is not implied as such)