This might seem like a basic question, but I've been stuck on this for a bit.
Upon looking at many different sources, I found 2 derivations of the rotation matrix.
- One of them considers a point at a distance of r from the origin and rotates it by a certain angle theta and derives the matrix by comparing the projections of the original point and the new, rotated point.
- The other one considers coordinate axes of unit length which are rotated by a certain angle theta and derives the rotation matrix by projecting the new x and y axes onto the original ones.
Which one of them is the correct derivation? What significance does each method have?