Catalog
Prerequisite Course
Linear Algebra
A rigorous treatment of linear algebra following Hefferon's acclaimed open textbook — from Gaussian elimination and vector spaces through linear maps, determinants, and eigendecomposition. Develops the theoretical foundations that underlie optimization, dimensionality reduction, and geometric transformations in modern ML.
Readings
1
Notation Reference
Symbolic conventions and Greek letter pronunciation used throughout these readings.
5 min
2
Linear Systems and Gauss's Method
Setting up linear systems in matrix form, row operations, echelon form, and Gaussian elimination.
18 min
3
Solution Sets and the Homogeneous Structure
Parametric solution form, the General = Particular + Homogeneous decomposition, and free variables.
16 min
4
Norms, Dot Products, and Angles
Euclidean length, dot product properties, Cauchy–Schwarz, angles and orthogonality, and ML applications including cosine similarity and distance metrics.
15 min
5
Vector Spaces and Subspaces
Vector space axioms, canonical examples, subspaces, and spanning sets.
17 min
6
Linear Independence and Bases
Independence, basis as the minimal spanning set, coordinate representation, and uniqueness.
16 min
7
Dimension
Invariance of basis size, dimensions of common spaces, rank-nullity, and combining subspaces.
14 min
8
Linear Maps: Isomorphisms and Homomorphisms
Structure-preserving maps, isomorphism as the right notion of sameness, range and null space.
16 min
9
Matrix Representations and Change of Basis
Encoding linear maps as matrices, matrix of a composition, similarity, and change-of-basis matrices.
17 min
10
Orthogonality and Projection
Orthogonal projection, Gram-Schmidt orthogonalization, projection into a subspace, and least squares.
18 min
11
Determinants
Permutation expansion, key properties, geometric interpretation as signed volume, Laplace's formula.
15 min
12
Eigenvalues, Diagonalization, and Jordan Form
Characteristic polynomial, diagonalizability, Jordan canonical form, and applications.
19 min
Quizzes
Linear Systems and Geometry
6 questions · 70% to pass
Vector Spaces and Dimension
6 questions · 70% to pass
Linear Maps, Change of Basis, and Projection
6 questions · 70% to pass
Determinants, Eigenvalues, and Spectral Structure
6 questions · 70% to pass
Labs
Geometry of Linear Transformations with Word Embeddings
45 min
SVD, PCA, and the Geometry of Neural Representations
60 min
Practice