← Playground
04
Matrix Transformations
A 2×2 matrix is a recipe for moving the whole plane. Change a number and the grid, the basis vectors and the shape all move with it.
PRESETS
î ↦ (1, 0) — the first column
ĵ ↦ (0, 1) — the second column
Identity: nothing moves
The pale dashed outline is the original shape; the solid one is its image. Every straight line stays straight and the origin never moves — that is all a matrix can do.
- det(A)
- 1
- Area scaling
- ×1
- Orientation
- preserved
- Invertible
- yes
- î ↦
- (1, 0)
- ĵ ↦
- (0, 1)
MATRIX
SHAPE