Things:

Math 108b: Advanced Linear Algebra

Course Information:

Professor: Padraic Bartlett.
Class Time/Location: MWF 9-9:50am, Psych 1902.
Office Hours: Thursdays, 2-3pm, South Hall 6516.
Email: padraic at math dot ucsb dot edu.
Syllabus: linked here.

Lecture Notes:

Week 1: Motivating eigenvalues, eigenvectors, and orthogonality.
Week 2: Change of basis.
Week 2: I was traveling this week. Therefore, lectures were recorded and placed on YouTube! They're kind of awkward, because lecturing without an audience is odd, but you can watch them here: part 1/3, part 2/3,part 3/3.
Week 3: Orthonormal bases.
Week 4: QR decomposition.
Week 4: Practice midterm!
Week 5: Markov processes and matrices.
Week 5: The Schur decomposition.
Weeks 6-7: Lies, inner product spaces, and the spectral theorem.
Week 8: Similar/elementary/permutation matrices.
Week 9-10: The Jordan Normal Form.
Week 10: Practice final!

Homework:

Set 1: Eigenvalues, eigenvectors, and orthogonality. Due Monday, January 13.
Set 2: Change of basis. Due Wednesday, January 22.
Set 3: Orthogonality. Due Monday, January 27.
Set 4: QR decompositions and Schur decompositions. Due Monday, February 10.
Set 5: Inner products and real symmetric matrices. Due Wednesday, February 19.
Set 6: Similar matrices and elementary matrices. Due Wednesday, February 26.
Set 7: Permutation matrices. Due Wednesday, March 5.
Set 8: Jordan normal form. Due Friday, March 14.