Schedule

Sixteen weeks, two hours each, 32 contact hours in total. Section and page numbers refer to Golub & Van Loan, Matrix Computations, 4th edition. Reading load is roughly 30 pages per week.

Click any week for objectives, algorithms, and materials.

Wk	Topic	Reading	Theme	Due
Foundations
1	Matrix multiplication as computation	§1.1–1.3 pp. 2–33	Cost	—
2	Matrix multiplication as computation	§1.1–1.3 pp. 2–33	Cost	—
3	Vector spaces, norms, and orthogonality	§2.1–2.3 pp. 64–76	Language	—
4	The singular value decomposition Key week	§2.4–2.5 pp. 76–87	Structure	—
5	Sensitivity and finite precision	§2.6–2.7 pp. 87–105	Conditioning	Assignment 1 — norms and conditioning
Linear systems
6	Triangular systems and the LU factorization	§3.1–3.2 pp. 106–122	Solve	—
7	Roundoff, pivoting, and accuracy	§3.3–3.5 pp. 122–144	Stability	—
8	Positive definite and banded systems	§4.1–4.3 pp. 154–186	Exploit structure	Assignment 2 — LU and Cholesky
9	Structured and fast solvers Midterm	§4.5, 4.7–4.8 pp. 196–233	Exploit structure	Midterm examination
Least squares
10	Householder, Givens, and the QR factorization	§5.1–5.2 pp. 234–260	Orthogonality	—
11	The full-rank least squares problem	§5.3–5.4 pp. 260–288	Fit	Assignment 3 — QR and least squares
12	Rank deficiency, regularization, and total least squares	§5.5, 6.1, 6.3 pp. 288–327	Regularize	—
Eigenvalues
13	Eigenvalue theory and perturbation	§7.1–7.2 pp. 348–365	Diagonalize	—
14	Power iterations and the QR algorithm	§7.3–7.5 pp. 365–394	Diagonalize	Assignment 4 — eigenvalues
15	Symmetric eigenproblems and computing the SVD Closes the loop from Week 3	§8.1–8.3, 8.6 pp. 440–467, 486–497	Diagonalize	—
Large scale
16	Sparse systems, conjugate gradient, and preconditioning	§11.1–11.3, 11.5, 10.1 pp. 598–639, 650–670, 546–556	Scale up	Assignment 5 — sparse and iterative methods
Synthesis
17	Matrix calculus, backpropagation, and synthesis	§12.3 pp. 707–719	Differentiate	Course project presentations

What is deliberately left out

A 32-hour course cannot cover a 747-page book. These are named in lecture but not examined, and each makes a good project topic:

Chapter 9, Functions of Matrices — the matrix exponential, sign, square root and logarithm.
Most of Chapter 10 — beyond the symmetric Lanczos process in Week 15.
§11.6, The Multigrid Framework — a natural follow-on to Week 15.
§12.1–12.2, 12.4–12.5 — displacement structure, structured-rank problems, and tensor decompositions.
Parallel sections (§1.6, §3.6) and the more specialised eigenvalue material (§7.6–7.9, §8.4–8.5, §8.7).