Planned schedule is tentative and may be adjusted depending on course progress.
GL are guest lectures.
Associated readings for each lecture are listed in the syllabus.

Unit 0: Fundamentals

Lecture	Date	Topics	Handouts	Dues
–		Course logistics	Logistics Introduction Unit 0 slides Unit 0 code Linear algebra review
1	Jan 21	Introduction; matrix–vector multiplication
2	Jan 23	Matrix–vector multiplication
3	Jan 26	Orthogonal vectors and matrices
4	Jan 28	Norms
5	Jan 30	Eigenvalues and eigenvectors
6	Feb 2	Computer arithmetic and matrix visualization

Unit 1: Singular value decomposition (SVD)

Lecture	Date	Topics	Handouts	Dues
7	Feb 4	SVD: geometric picture, definitions	Unit 1 slides Unit 1 code SVD notes	HW1 (Feb 3)
8	Feb 6	SVD: matrix properties
9	Feb 9	SVD: low-rank approximation, image processing
10	Feb 11	Principal component analysis (PCA)
11 (GL)	Feb 13	SVD and PCA: extensions, applications

Unit 2: QR factorization and least squares

Lecture	Date	Topics	Handouts	Dues
12	Feb 16	Projectors	Unit 2 slides Unit 2 code QR notes	HW2 (Feb 17)
13	Feb 18	QR factorization Projectors
14	Feb 20	QR factorization
15	Feb 23	Gram–Schmidt orthogonalization
16	Feb 25	Householder triangularization
17	Feb 27	Least squares problems

Unit 3: Conditioning and stability

Lecture	Date	Topics	Handouts	Dues
18	Mar 2	Conditioning and condition numbers	Unit 3 slides Unit 3 code	HW3 (Mar 3 Mar 5)
19	Mar 4	Stability Conditioning
20 (GL)	Mar 6	Condition numbers and stability
21	Mar 9	Stability

Unit 4: Linear systems

Lecture	Date	Topics	Handouts	Dues
–	Mar 11	Mid-term exam	Unit 4 slides Unit 4 code
22	Mar 13	Gaussian elimination and LU factorization
23 (GL)	Mar 16	Pivoting
24 (GL)	Mar 18	Cholesky factorization
25 (GL)	Mar 20	Complexity and timing algorithms

Unit 5: Eigenvalue problems

Lecture	Date	Topics	Handouts	Dues
26	Mar 23	Eigenvalue problems and definitions	Unit 5 slides Unit 5 code	HW4 (Mar 24)
27	Mar 25	Gershgorin theorem, eigenvalue sensitivity
28	Mar 27	Overview of eigenvalue algorithms, Hessenberg reduction
–	Mar 30	Spring break
–	Apr 1	Spring break
–	Apr 3	Spring break
29	Apr 6	Power method
30	Apr 8	Inverse iteration, Rayleigh quotient
31	Apr 10	QR algorithm without shifts

Unit 6: Iterative methods

Lecture	Date	Topics	Handouts	Dues
32	Apr 13	Overview of iterative methods	Unit 6 slides Unit 6 code CG notes	HW5 (Apr 14)
33	Apr 15	Arnoldi iteration
34	Apr 17	More on Arnoldi iteration
35	Apr 20	Lanczos iteration
36	Apr 22	GMRES
37	Apr 24	More on GMRES
38	Apr 27	Preconditioning GMRES and Conjugate gradient		HW6 (Apr 28)
39	Apr 29	More on CG
40	May 1	Course review