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Linear algebra
The mathematics of many things at once.
A vector is a list of numbers treated as one object; a matrix transforms whole collections of them in a single move. Linear algebra is how mathematics handles a thousand variables with the same ease as one.
Your progress
9 lessons
The big ideas
Vectors are arrows and lists
One object, two views: an arrow with direction and length, or a column of coordinates. Fluency means switching between them freely.
Matrices are verbs
A matrix isn't a grid of numbers to stare at — it's an action: rotate, stretch, project, shear. Multiplying applies the action.
Eigenvectors are the grain of a transformation
Most vectors get knocked off course by a transformation. A few special ones only stretch. Find them and you've found the transformation's skeleton.
The course — start at lesson one
- 01VectorsArrows, lists, addition, scaling — the atoms.Medium
- 02The dot productOne number that measures alignment.Medium
- 03Matrices as transformationsWatch the plane move — verbs for space.Medium
- 04Solving systems & why it scalesMany unknowns, one act — determinants, inverses, elimination.Medium
- 05Orthogonality, projections & least squaresThe geometry of best guesses — and the engine of Fourier analysis.Medium
- 06Eigenvectors in actionStubborn directions, long-run behavior, and PageRank.Medium
- 07Norms & distanceThe rulers of ML: lengths, L1 vs L2, and similarity.Medium
- 08Rank & the four subspacesIndependent directions, null space, and why data is low-rank.Medium
- 09Matrix decompositions & SVDLU/QR/Cholesky, and SVD for compression, PCA, and recommendation.Hard
Out in the world
Machine learning
Data is matrices; models are matrix operations. GPUs exist because of linear algebra.
3D graphics
Every camera move and object rotation in a game is a 4×4 matrix multiplication.
Search & recommendations
PageRank and recommender systems are eigenvector problems at web scale.
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