Algebra·Course
Linear Algebra
Linear algebra: vector spaces, matrices, determinants, eigenvalues, linear transformations, and ML applications
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Solve linear systems with matrices.
- 02Think in terms of vector spaces and bases.
- 03Find and use eigenvalues and eigenvectors.
- 04Apply linear algebra to real problems (ML, graphics, data).
- 05Read a transformation geometrically.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~2 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Linear Algebra [Online course]. Stoa. https://stoa.school/course/algebra
- MLA
Stoa. “Linear Algebra.” Stoa, 2026, https://stoa.school/course/algebra.
- Chicago
Stoa. “Linear Algebra.” Stoa. Accessed September 1, 2026. https://stoa.school/course/algebra.
§ 02 — Curriculum
8 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IComplex Numbers, Matrices, and DeterminantsComplex numbers, matrix operations, determinants and their properties3 articles
18 minBegin → - M IIGroups, Rings, and FieldsBasic algebraic structures and their properties3 articles
18 minBegin → - M IIIVector SpacesBasis, dimension, linear maps, matrix of a linear map3 articles
18 minBegin → - M IVLinear Operators and the Jordan FormInvariants of operators, Jordan normal form3 articles
18 minBegin → - M VEuclidean and Unitary SpacesInner product, orthogonalization, self-adjoint operators3 articles
18 minBegin → - M VITensor AlgebraMultilinear forms, tensor product, tensors in physics3 articles
18 minBegin → - M VIIGroup Theory: Sylow TheoremsNormal subgroups, Sylow theorems, solvable groups3 articles
18 minBegin → - M VIIITensor Algebra and Sylow Theorems (Advanced)Modules, categories, homological algebra3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Solve systems of linear equations using Gaussian elimination and compute determinants.
Work with bases, dimension, and linear mappings.
Find eigenvalues and eigenvectors and diagonalize matrices.
Apply linear algebra to problems in data analysis, optimization, and physics.
§ 04 — Practices