Matrices are transformations of space. Every matrix describes where the basis vectors î and ĵ land after the transformation.
- • 02:14 — A linear transformation keeps gridlines parallel and evenly spaced, and keeps origin fixed.
- • 05:31 — î lands on column 1 of the matrix; ĵ lands on column 2.
- • 09:47 — Matrix-vector multiplication = scaled sum of the transformed basis vectors.
- • 12:20 — Composition of transformations = matrix multiplication (read right-to-left).