Course · Beginner
Linear Algebra for Machine Learning
Vectors, matrices and the geometry hiding inside every model.
Every image, sentence and user in machine learning becomes a vector, and every layer of a network is a matrix. This course builds linear algebra from the ground up with geometry first: vectors and dot products, span and basis, matrices as transformations, elimination, rank, projections, eigenvectors and the SVD. Each chamber runs the research loop, from discovery to derivation to real papers such as PageRank, LoRA and PCA, with proofs to write and problems to code. Talos, the bronze guardian of Crete, waits at the centre.
- Chambers
- 9 + boss
- Time
- ~8 hours
- Questions
- 106
- Coding problems
- 27
- Concept cards
- 37
- XP available
- 5,690+
Cleared You are here Ahead
The path through the labyrinth
Three rings, 9 chambers, one guardian. You can wander ahead, but the thread works best in order: each chamber builds on the last.
Ring I
The Outer Ring
Vectors and their geometry- 1Vectors: Arrows, Lists and DataYou are hereTwo views of the same object, and why every image, word and user in ML becomes a vector. 35 min 50 XP12 questions
- 2Dot Products, Lengths and AnglesMeasure similarity with one multiplication: norms, angles, cosine similarity and projections. 40 min 60 XP12 questions
- 3Span, Basis and DimensionWhich points can you reach? Linear independence, bases and the true dimension of your data. 40 min 60 XP12 questions
Ring II
The Middle Ring
Matrices as machines- 4Matrices as TransformationsA matrix is a function that moves space. Watch grids rotate, shear and collapse, then compose them. 40 min 60 XP12 questions
- 5Solving Systems: Elimination and InversesGaussian elimination, pivots, inverses and determinants: when can you undo a matrix? 40 min 60 XP11 questions
- 6Rank and the Four SubspacesColumn space, null space and rank–nullity: what a matrix keeps, what it destroys, and why LoRA works. 40 min 60 XP11 questions
Ring III
The Inner Ring
The hidden structure- 7Orthogonality and Least SquaresProjections, orthonormal bases and the normal equations: linear regression, derived with geometry. 45 min 60 XP12 questions
- 8Eigenvectors and EigenvaluesThe directions a matrix only stretches: characteristic polynomials, power iteration and PageRank. 45 min 60 XP12 questions
- 9SVD and PCA: The Shape of DataEvery matrix is a rotation, a stretch and a rotation. Compress images and find the principal components of data. 45 min 60 XP12 questions
The centre
Talos, the Bronze GuardianA giant of bronze circles the island, driven by one vein of ichor. Find the structure beneath the metal to bring him down.8 hits to win · 3 lives+300 XP · +100 flawless bonus · certificate