This is an advanced course in applied linear algebra. The goal is to give students both the mathematical depth and the practical tools needed to tackle the kinds of estimation, fitting, and optimization problems that come up constantly in engineering and research. Topics include range and null spaces, orthogonality, QR factorization, least-squares and least-norm methods, eigenvalues, symmetric matrices, the singular value decomposition, Gaussian distributions, and MMSE estimation. Throughout, the emphasis is on understanding what these tools are actually doing and why they work, not just on how to apply them mechanically. Applications are drawn from a broad range of disciplines, including signal processing, machine learning, control systems, navigation, circuits, finance, and portfolio optimization.
Prerequisites: Linear algebra as in Engr 108 or Math 104, and basic probability.
Tuesdays and Thursdays, 9:00am - 10:50am
First lecture 6/23, last lecture 8/13
Location: Skilling Auditorium
This class will be taught live. All lectures will also be recorded (by SCPD/CGOE) and the videos will be posted on Canvas approximately one hour after the class ends.
A good reference for an introductory treatment of some parts of the course is the book Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares by Stephen Boyd and Lieven Vandenberghe. This is the textbook for engr108, and is available online.
The book is not required, and EE263 differs from the book. EE263 is at a more advanced level, and it covers much material that is not in the book. Complete notes for this class will be available online. See the section on reading for other references.
In previous years, EE263 was titled Introduction to Linear Dynamical Systems and covered both an application-oriented approach to linear algebra and an introduction to linear dynamical systems. Starting in Fall 2025, that course was split into two. The first is EE263: Matrix Methods: Singular Value Decomposition, which covers an expanded version of the linear algebra from the old EE263, with the same emphasis on applications and on how to formulate and solve a broad range of practical problems using these tools. The second is EE363: Linear Dynamical Systems, which provides more in-depth coverage of the dynamical systems material from the old EE263. The new EE263 provides good background for both EE363 and EE364a.
If you have taken the old EE263, you cannot (and should not) take this new version too. But you may wish to take EE363 in Spring.
This course was originally developed and taught by Professor Stephen Boyd. The material from this version of the course, and the complete set of materials consisting of lecture videos, slides, support notes and homework is still available in the archive. This version substantially differs from the current version.