EE 263: Matrix Methods
About the Course
I served as the instructor for this course over three summers (2023, 2024, 2025) at Stanford. Below you’ll find materials from the Summer 2025 offering, including the raw lecture slides as well as the annotated slides from my lectures. I have also included the problem sets and final exam, but have not included solutions as these questions are often reused in new offerings of the class.
The course covers linear algebra and matrix methods with a strong emphasis on engineering applications, including topics such as least squares, eigenvalue decomposition, QR factorization, Singular Value Decomposition, and foundations of linear dynamical systems.
Note that before Fall 2025, this course was titled “Introduction to Linear Dynamical Systems.” Starting Fall 2025, the content was split into two courses: EE 263: Matrix Methods now focuses primarily on linear algebra and SVD, while a new course, EE 363: Linear Dynamical Systems, covers dynamical systems topics from the old EE 263 along with more advanced material. The latest version of EE 263 is always available at ee263.stanford.edu.
Interactive Simulations
Open the EE263 interactive simulations.
Course Materials (Summer 2025)
Lectures
| # | Topic | Slides | Annotated |
|---|---|---|---|
| 1 | Overview | ||
| 2 | Linear functions | ||
| 3 | Engineering examples | ||
| 4 | Interpretations of linear equations | ||
| 5 | Linear algebra review | ||
| 6 | Range and null space | ||
| 7 | Rank | ||
| 8 | Orthogonality | ||
| 9 | QR factorization | ||
| 10 | Least-squares | ||
| 11 | Multi-objective least-squares | ||
| 12 | Least-norm solutions of underdetermined equations | ||
| 13 | Recursive estimation | ||
| 14 | Least-squares fitting | ||
| 15 | LS via QR factorization | ||
| 16 | Gauss-Newton method | ||
| 17 | Eigenvectors and diagonalization | ||
| 18 | Symmetric matrices | ||
| 19 | Ellipsoids | ||
| 20 | Matrix norm | ||
| 21 | SVD and applications | ||
| 22 | Autonomous linear dynamical systems | ||
| 23 | Solution via matrix exponential | ||
| 24 | Dynamic interpretation of eigenvectors |
Homework
| # | Problem Set |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 |