# ENGR108: Introduction to Matrix Methods

John Duchi and Babak Ayazifar, Stanford University, Fall 2023

## Syllabus

In this course, we will focus (of course) on vectors, matrices, and their applications, with a special emphasis on those we can understand and solve via least-squares problems. Lectures will consist of going through slides, on which we will actively take notes, and we will post the handwritten notes here.

A rough outline of topics we expect to cover is as follows:

• Vectors: definitions, operations on vectors, distances, norms, and applications in clustering.

• Matrices: definitions, examples, basic factorizations and their uses, examples via dynamical systmes.

• Least squares: definitions of the problem, applications in data fitting, control, and investment

## Lectures and Reading

Here, we will post readings from the course textbook associated with each lecture. In addition, for posterity's sake, we post a few annotated lecture slides from previous iterations of the course, though their similarity with this year's version may vary.

 Topic Reading Slides Tue, April 4 Overview and vectors Ch. 1 Overview, vectors Thu, April 6 Vectors and linear functions Chs. 1–2 vectors, linear functions Tue, April 11 Linear functions and norms Chs. 2–3 linear functions Thu, April 13 Norms and clustering Chs. 3–4 norms Tue, April 18 Clustering Ch. 4 clustering Thu, April 20 Linear independence Ch. 5 linear independence Tue, April 25 Bases and Gram Schmidt Ch. 5 linear independence Thu, April 27 Matrices Ch. 6 matrices Tue, May 2 Matrices Ch. 6 matrices Thu, May 4 Midterm Chs. 1–6 Tue, May 9 Matrix examples Ch. 7 examples Thu, May 11 Matrix examples Ch. 7 examples Tue, May 16 Linear equations Ch. 8 equations Thu, May 18 Matrix multiplication Ch. 10 multiplication Tue, May 23 Matrix multiplication and inverses Chs. 10–11 multiplication, inverses Thu, May 25 Matrix inverses Ch. 11 inverse Tue, May 30 Least squares Ch. 12 least squares Thu, June 1 Least squares data fitting Ch. 13 fitting Tue, June 6 Least squares data fitting Ch. 13 fitting