🎬Visualize the curvilinear coordinate through Cartesian grid and a polar coordinate system in a Eucli

The physical world is independent of the coordinate system you use to describe it. A vector field, like the radial field in this demo, is a physical reality. However, its mathematical representation—the components of the vector—changes depending on the coordinate system you choose. choosing the right coordinate system simplifies the problem. For a system with circular symmetry, the vector field is constant and simple in polar coordinates but complex and variant in Cartesian coordinates. This shows that the perceived "complexity" of a problem can often be a consequence of the descriptive language (the coordinate system) rather than the physical reality itself.

The Outer Product and Tensor Transformations | Condensed Notesviadean on Notion