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M03 · Linear Algebra II: Decompositions

A free, illustrated L2 course of 10 modules in the Mathematics track. Modules include: Eigenvalues and eigenvectors; Diagonalization and matrix powers; Symmetric matrices and the spectral theorem.

M03 L2 · Intermediate 10 modules · about 40 lessons Planned · Ring 2

Part of the Mathematics track. Ships in Ring 2 (Spine) of the roadmap.

Modules

1. Eigenvalues and eigenvectors
2. Diagonalization and matrix powers
3. Symmetric matrices and the spectral theorem
4. Positive definite matrices and quadratic forms
5. Singular value decomposition
6. Low-rank approximation and PCA
7. Least squares and the pseudoinverse
8. Matrix norms and conditioning
9. Markov matrices, graphs and PageRank
10. Tensors and index notation for deep learning

Signature illustrations

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

Eigenvectors staying on their line, SVD as rotate, stretch, rotate, image compression by rank, bowls and saddles of quadratic forms, least squares as projection.

Status

This course is planned, not written yet. It ships with Ring 2 (Spine).

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.