vectors and tensors
vectors and tensors the dependency chain that makes vectors and tensors necessary, rather than around historical chronology. The original sequence runs algebra → calculus → vectors → quaternions → Maxwell → vector analysis → spacetime → curvature → tensors → relativity. TOC Part I — Representation Debt Scalar description 1.1 Magnitude-only quantities 1.2 Why one number is insufficient 1.3 Physical versus informational dimensions 1.4 SOURCE ≠ coordinate description Coordinates and components 2.1 Coordinate systems 2.2 Basis choice 2.3 Components as representation 2.4 Object versus component list 2.5 Representation change as the first GRM transport problem Part II — Vector Necessity Vector space 3.1 Addition and scalar multiplication 3.2 Linear independence 3.3 Dimension 3.4 Basis and coordinate expansion 3.5 Directed physical quantities as one application, not the definition Change of basis 4.1 Same vector, different components 4.2 Transformation matrices 4.3 Equivalence across rep...