TwiddleLab / Courses / Math
Vectors and Matrices
Arrows that move things and matrices that bend the whole grid, built by hand.
Best after: Functions You Can See, Algebra in Motion
Lessons
- Arrows That Move Things (5 min): A vector is a move: how far across and how far up.
- How Long Is an Arrow? (7 min): The length of (x, y) comes from the squares on its legs: length² = x² + y².
- Adding Arrows (7 min): To add arrows, put them tip to tail. The sum goes from the first tail to the last tip.
- Stretching Arrows (7 min): Multiplying an arrow by a number k is a scalar multiple: k(x, y) = (kx, ky).
- Recipes of Arrows: Linear Combinations (7 min): A linear combination of a and b is a recipe s a + t b: stretch each, then add tip to tail.
- How Much Together: Dot Product (7 min): The dot product of a and b is a₁b₁ + a₂b₂: multiply in pairs, then add.
- A Matrix Moves the Grid (7 min): A linear transformation moves the whole plane at once.
- Read a Matrix by Its Columns (7 min): A linear move is decided by where i hat = (1, 0) and j hat = (0, 1) land.
- Two Moves in a Row (7 min): Two moves in a row are one move: the product B A means first A, then B.
- Area Scaling: the Determinant (7 min): The determinant of [[a, b], [c, d]] is ad - bc: how many times bigger every area gets.
- Undoing a Matrix (7 min): The inverse A⁻¹ undoes A: A⁻¹ A = I, the do-nothing matrix.
- Project: Pixel Art Transformer (8 min): Every move of a sprite is a 2 by 2 matrix: read its columns to build it.
Lessons are interactive and need JavaScript. Turn it on to play them.
