> "Don’t think of them as rotations, think of them as a unit vectors of a new coordinate systems." That's exactly what all square non-singular matrices with un

> "Don’t think of them as rotations, think of them as a unit vectors of a new coordinate systems." That's exactly what all square non-singular matrices with unit column spaces are. In fact, all square non-singular matrices are coordinate transformations. That's pretty much the central point of linear algebra. Framing rotation matrices as changes to the coordinate system doesn't add much info like framing polynomials as continuous functions. Technically it's true, but it doesn't add much to clarify.