This course is about how to solve, computationally, linear algebra problems. It is not a course to introduce linear algebra (you are expected to already have some background in this - see prerequisites), although we will review this material as needed and you might be asked to demonstrate understanding of this. It is also not a course on the applications of linear algebra. (For that, you could take COSC 36/136, for example.) Rather, it is on how to solve those linear algebra problems that you get in your applications: we will study the algorithms of linear algebra. Or, to quote one of the authors of our textbook (see the Appendix)

``Numerical analysis is the study of algorithms for the problems of continuous mathematics.''

Please read the Appendix of the text book before the second class for a much more insightful and thorough discussion about what this course is about.

This is a rough and tentative syllabus, that I have essentially copied from the textbook we are using.

• orthogonal vectors, norms, singular value decomposition
• QR factorization, Gram-Schmidt orthogonalization, and least squares problems
• conditioning and stability
• Gaussian elimination and Cholesky factorization
• eigenvalue problems, Raleigh quotient, QR algorithm
• iterative methods: Arnoldi, Lanczos, conjugate gradient
• preconditioning

This is the main text book. We will also use supplementary material.

L. N. Trefethen and D. Bau. Numerical Linear Algebra, SIAM, 1997.

Familiarity with linear algebra and with computers; "mathematical maturity"

There will be weekly homeworks, and two exams in this course. The homeworks will involve a mix of problem solving, proving, and programming in Matlab.