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M02 · Linear Algebra I: Vectors and Matrices

A free, illustrated L1 course of 10 modules in the Mathematics track. Modules include: Vectors as arrows and as data; Linear combinations, span and basis; Dot product, norms, angles and projections.

M02 L1 · Core 10 modules · about 40 lessons 10 of 10 modules live

Part of the Mathematics track. Ships in Ring 1 (Foundation) of the roadmap.

Modules

1. Vectors as arrows and as data Live · 4 lessons
2. Linear combinations, span and basis Live · 4 lessons
3. Dot product, norms, angles and projections Live · 4 lessons
4. Matrices as linear maps Live · 4 lessons
5. Matrix multiplication as composition Live · 4 lessons
6. Linear systems and elimination Live · 4 lessons
7. Inverses, rank and the four subspaces Live · 4 lessons
8. Determinants as volume scaling Live · 4 lessons
9. Change of basis Live · 4 lessons
10. Orthogonality, Gram-Schmidt and QR Live · 4 lessons

Signature illustrations

The pictures a learner should still see in their head a year later:

Grid-warping transformations, span sweeping out a line or plane, projection shadows, the four-subspaces picture, determinant as area scaling.

Status

10 of 10 modules are written and live. The rest follow in Ring 1.

Every lesson will follow the same twelve-part blueprint with at least three purpose-made figures. Watch the repository to hear when modules ship, or help write and review it.