Applications of Linear Algebra
Math 2LA3, Summer 2024
The course webpage is on Avenue, all information will be posted there.
Schedule
- Lectures: Mondays and Wednesdays 7–10pm
- Office hours: See Avenue
Our first class is Monday, June 24 — see you then! Office hours start Wednesday, June 26.
We will cover the following topics:
- Linear programming: geometric and simplex methods
- Dynamical systems: basics of differential equations, eigenvalues, eigenvectors, diagonalization
- Orthogonality: dot product, distance, projection, QR factorization, distance minimization, least squares, linear models
- Optimization of quadratic forms: diagonalization of symmetric matrices, Spectral theorem, quadratic forms
- Singular value decomposition: existence and construction, pseudoinverses, least squares, principal component analysis, image compression
- Markov chains: equilibria, long-run behaviour, PageRank
Course Materials
The main references for the course are the Course Notes and the 6th edition of Linear Algebra and Its Applications by D. C. Lay, S. R. Lay, and J. J. McDonald.
Assignments
| Assignment | Topics |
|---|---|
| Geometry of linear programs. Simplex method for canonical linear programs. | Assignment 1 |
| Simplex method for noncanonical linear programs. Diagonalization, dynamical systems. | Assignment 2 |
| Dot product, orthogonality, Gram-Schmidt. QR factorization. | Assignment 3 |
| Least squares problems. Lines of best fit. Quadratic forms. Orthogonal diagonalization. Spectral Theorem. | Assignment 4 |
| Optimization and classification of quadratic forms. Singular value decomposition and applications to least squares. | Assignment 5 |
| Covariance. Principal component analysis. Image compression. Markov chains, PageRank. | Assignment 6 |