Latest information:
- A useful reference for our discussion on self-adjoint, normal, and unitary operators, along with a primer on singular value decomposition, are chapters 6 and 7 of "Linear Algebra Done Right," by S. Axler (available here). Although the notation differs slightly from ours, the text is a very elegant and readable survey of the topics we cover.
- Brin and Page's original articles on PageRank are available here and here. A discussion on the convergence rate of PageRank using a bound on the second eigenvalue can be found here (as well as in the lecture notes). Finally, an introduction to networks, centrality measures, etc., can be found here (from "Networks: an introduction," by M. Newman).
- I've posted a short discussion on one particular example of a Markov chain (a random walk on a finite state space), which is available here. Please e-mail me if you'd like the code used to generate the figures shown.
- The course syllabus is now online. The supplementary textbook we will be using ("Linear Algebra Done Wrong," by S. Treil) is available for download here.
Lecture notes:
These materials are from a previous version of this course. Please ignore all references to lecture dates, and note that the order of topics covered may vary slightly.- Week 1 (introduction, vector spaces, basis)
- Week 2 (coordinate representation, change of basis, linear transformations)
- Week 3 (matrix representation, effect of change of basis, kernel and range)
- Week 4 (eigenvalues, eigenvectors, diagonalization)
- Week 5 (complexification, multiplicity of eigenvalues)
- Week 6 (Jordan canonical form)
- Week 7 (linear evolution equations)
- Week 8 (long-time behavior, Markov chains)
- Week 9 (Markov chains (cont'd), applications to network science)
- Week 10 (inner product spaces)
- Week 11 (projections, Gram-Schmidt orthogonalization)
- Week 12 (least squares, adjoints, self-adjoint operators)
- Week 13 (normal operators, spectral theorem, isometries)
- Week 14 (singular value decomposition, applications of SVD)
- Week 15 (Fourier series, applications to linear PDE)
Homework assignments:
- Homework #1 (due Tue., Jan. 22) [solutions]
- Homework #2 (due Tue., Jan. 29) [solutions]
- Homework #3 (due Tue., Feb. 05) [solutions]
- Homework #4 (due Tue., Feb. 12) [solutions]
- Homework #5 (due Tue., Feb. 26) [solutions]
- Homework #6 (due Thu., Mar. 07) [solutions]
- Homework #7 (due Thu., Mar. 21) [solutions]
- Homework #8 (due Thu., Mar. 28) [solutions]
- Homework #9 (due Tue., Apr. 09) [solutions]
- Homework #10 (due Tue., Apr. 16) [solutions]
- Homework #11 (due Tue., Apr. 23) [solutions]
- Homework #12 (due Tue., Apr. 30) [solutions]
- Homework #13 (due Tue., May 07) [solutions]
Exam solutions:
- Midterm #1 (Tue., Feb. 19)
- Midterm #2 (Thu., Apr. 05)
- Final exam (Sat., May 11)