🎬a tensor as a physical object that exists independently of the coordinate system used to describe it

The animation shows that while the numerical components of a tensor depend entirely on the chosen coordinate system, the physical object it represents (the ellipse) does not change. A tensor is the underlying object, and its components are simply a mathematical description of that object in a given basis.

Transformation of the Inverse Metric Tensor | Proof and Derivationviadean on Notion