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 written up a short discussion on one particular example of a Markov chain (a random walk on a finite state space), which is available here (updated 03/07). 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:
- 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, linear evolution equations)
- Week 7 (linear evolution equations (cont'd), long-time behavior)
- Week 8 (Markov chains, applications to network science)
- Week 9 (inner product spaces, duality)
- Week 10 (projections, Gram-Schmidt orthogonalization, least squares)
- Week 11 (adjoints, self-adjoint and normal operators, spectral theorem)
- Week 12 (isometries, positive operators, singular value decomposition)
- Week 13 (applications of SVD, infinite-dimensional spaces, Fourier series)
- Week 14 (Fourier series (cont'd), applications to linear PDE)
- Week 15 (continuous spectrum, Dirac distribution, Fourier transform)
Homework assignments:
- Homework #1 (due Wed., Jan. 25) [solutions]
- Homework #2 (due Wed., Feb. 01) [solutions]
- Homework #3 (due Wed., Feb. 08) [solutions]
- Homework #4 (due Fri., Feb. 17) [solutions]
- Homework #5 (due Fri., Feb. 24) [solutions]
- Homework #6 (due Fri., Mar. 02) [solutions]
- Homework #7 (due Fri., Mar. 09) [solutions]
- Homework #8 (due Wed., Mar. 21) [solutions]
- Homework #9 (due Fri., Mar. 30) [solutions]
- Homework #10 (due Fri., Apr. 06) [solutions]
- Homework #11 (due Fri., Apr. 13) [solutions]
- Homework #12 (due Mon., Apr. 23) [solutions]
- Homework #13 (due Fri., May 4) [solutions]
Exam solutions:
- Midterm #1 (Mon., Feb. 13)
- Midterm #2 (Fri., Mar. 23)
- Midterm #3 (Wed., Apr. 25)
- Final exam (Sat., May 12)
Sample exams:
- Sample midterm #1, solutions
- Sample midterm #2, solutions
- Sample midterm #3, solutions
- Sample final exam, solutions