ENGR108: Introduction to Matrix Methods
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. We encourage students to take notes on
their own printed copy of the slides.
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.
Lectures and Reading
Here, we will post readings from the
course textbook associated with
each lecture.
| Topic | Reading | Slides |
| Tue, Sep 22 | Overview and vectors | Ch. 1 | Overview, vectors |
| Thu, Sep 24 | Linear functions and norms | Chs. 2–3 | linear functions, norms |
| Tue, Sep 29 | Norms and clustering | Chs. 3–4 | norms, clustering |
| Thu, Oct 1 | Clustering and linear independence | Chs. 4–5 | clustering, linear independence |
| Tue, Oct 6 | Linear independence | Ch. 5 | linear independence |
| Thu, Oct 8 | Linear independence, matrices | Chs. 5–6 | matrices |
| Tue, Oct 13 | Matrices and examples | Chs. 6–7 | matrices, examples |
| Thu, Oct 15 | Matrix examples, linear eqs | Chs. 7–8 | examples, linear equations |
| Tue, Oct 20 | Linear eqs, dynamical systems | Chs. 8–9 | linear equations, dynamical systems |
| Thu, Oct 22 | Matrix multiplication | Ch. 10 | matrix multiplication |
| Tue, Oct 27 | Midterm | Chs. 1–10 | |
| Thu, Oct 29 | Matrix multiplication and QR factorization | Ch. 10 | matrix multiplication |
| Tue, Nov 3 | Matrix inverses | Ch. 11 | inverses |
| Thu, Nov 5 | Inverses and least squares | Chs. 11–12 | inverses, least squares |
| Tue, Nov 10 | Least squares, data fitting | Chs. 12–13 | least squares, regression fitting |
| Thu, Nov 12 | Data fitting and classification | Chs. 13–14 | regression, classification |
| Tue, Nov 17 | Classification and constraints | Chs. 14, 16 | classification, constrained least squares |
| Thu, Nov 19 | Constrained least squares | Ch. 16 | constrained least squares |
| Tue, Dec 1 | Constrained LS applications | Ch. 17 | CLS applications |
| Thu, Dec 3 | Review | Chs. 1–17 |
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