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.
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 |
| Mon, Sep 23 | Overview and vectors | Ch. 1 | Overview, vectors |
| Wed, Sep 25 | Linear functions and norms | Chs. 2–3 | linear functions, norms |
| Mon, Sep 30 | Norms and clustering | Chs. 3–4 | norms, clustering |
| Wed, Oct 1 | Clustering and linear independence | Chs. 4–5 | clustering, linear independence |
| Mon, Oct 7 | Linear independence | Ch. 5 | linear independence |
| Wed, Oct 9 | Linear independence, matrices | Chs. 5–6 | matrices |
| Mon, Oct 14 | Matrices and examples | Chs. 6–7 | matrices, examples |
| Wed, Oct 16 | Matrix examples, linear eqs | Chs. 7–8 | examples, linear equations |
| Mon, Oct 21 | Linear eqs, dynamical systems | Chs. 8–9 | linear equations, dynamical systems |
| Wed, Oct 23 | Matrix multiplication | Ch. 10 | matrix multiplication |
| Mon, Oct 28 | Midterm | Chs. 1–10 | |
| Wed, Oct 30 | Matrix multiplication and QR factorization | Ch. 10 | matrix multiplication |
| Mon, Nov 4 | Matrix inverses | Ch. 11 | inverses |
| Wed, Nov 6 | Inverses and least squares | Chs. 11–12 | inverses, least squares |
| Mon, Nov 11 | Least squares, data fitting | Chs. 12–13 | least squares, regression fitting |
| Wed, Nov 13 | Data fitting and classification | Chs. 13–14 | regression, classification |
| Mon, Nov 18 | Classification and constraints | Chs. 14, 16 | classification, constrained least squares |
| Wed, Nov 20 | Constrained least squares | Ch. 16 | constrained least squares |
| Mon, Dec 2 | Constrained LS applications | Ch. 17 | CLS applications |
| Wed, Dec 4 | Review | Chs. 1–17 |
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