Linear Algebra· Study notes
Algebra
Matrices, vector spaces and linear maps, determinants, eigenvalues and diagonalization, orthogonality and least squares, quadratic forms, the SVD, and Markov chains.
What you'll be able to do
- Solve linear systems by row reduction and read off the solution set
- Find eigenvalues and diagonalize
- Project onto subspaces and fit least-squares models
- Interpret the SVD
Read the notes as a guided lesson
Walk the notes one box at a time — prose, worked examples, quick checks — with a timed practice round after every section. For the full course with interactive lessons, go back to the course.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics
Row Reduction & Rank
5 lessonsGaussian elimination and the shape of solution sets
Determinants & Inverses
5 lessonsOne number that decides invertibility
Vector Spaces & Bases
5 lessonsSpan, independence, basis, dimension
Linear Transformations
5 lessonsKernel, image, rotations and reflections
Orthogonality & Least Squares
5 lessonsProjections, distance, and best fit
Eigenvalues
5 lessonsThe directions a matrix merely stretches
Diagonalization & Matrix Powers
5 lessonsA = PDP⁻¹ and everything it unlocks
Symmetric Matrices & Quadratic Forms
5 lessonsThe spectral theorem and definiteness
Singular Values & the SVD
5 lessonsEvery matrix is rank-one layers, sorted by importance
Markov Chains & Long-Run Behavior
5 lessonsSteady states, mixing, and absorbing states