Math 420: Advanced Linear Algebra

Professor: David E Speyer, speyer@umich.edu
Class: 3437 Mason Hall, Tuesday and Thursday, 8:30-10:00 AM.
Office hours: 2844 East Hall, Tuesdays 2-5 PM, Thursdays 12-3 PM. At the moment I am planning to have all office hours open to all my courses; if this is a problem, we'll adjust. If you'd like to meet on Zoom, send an e-mail and I'll be glad to log on.
Problem Sets due: Thursday nights at Midnight, on Gradescope.
Textbook: Linear Algebra, Hoffman and Kunze (2nd edition).

Climate: Each of you deserves to learn in an environment where you feel safe and respected.
I want our classroom, the collaborations between my students outside class, and the mathematics department as a whole, to be an environment where students feel able to share their ideas. I want to provide a space where questions are very welcome, especially on basic points.
Please ask all questions you have; remember that every question you have is likely a question that many share. Please share your insights and suggestions, partial or complete. Please treat your peers questions, comments and ideas with respect.

Grading: Your final grade will be made out of 25% Midterm 1, 25% Midterm 2, 25% Final Exam and 25% Homework. I will drop the two lowest homeworks.
Reading: I will assign reading in the textbook. You are responsible for doing this reading in advance of class. This will allow me to use class time more efficiently to clear up points of confusion and present alternate perspectives.
Exams: We will have two evening exams, on the evenings of Thursday, February 10 and ~~Thursday, March 24~~ Tuesday, March 29, from 6:00-8:00 PM. Please be sure to keep these evenings clear. Our final exam will be Thursday, April 28, 10:30 AM-12:30 PM. If you have a medical condition requiring special accomodation during exams, please inform me and provide medical documentation from the Services for Students with Disabilities (SSD) office as soon as possible.
Homework Policies: In computational questions, include your work to show how the computation was done; in proof questions, give a complete, correct argument in full English sentences.
You may collaberate on homework, but you must write up and turn in your own problem set, and you must disclose any people with whom you worked.
You are free to seek help from me, from each other (disclosed as above), and from the tutors at the Mathlab. You absolutely MAY NOT post homework problems to internet discussion boards. If you get help from someone outside this group, it should be limited in nature, and must be disclosed.

Schedule of readings and assignments: Problem sets are due at 11:59 PM on Thursday of the corresponding week. I will be flexible about extensions for illness if you ask before the assignment is due. Begin reading during the corresponding week and complete it before Thursday's class. In most weeks, I will put up a poll to ask for questions from the reading.
Plans for future weeks are my best estimate of my schedule but are not guaranteed. I will not change assignments (except to correct errors) once they are less than one week from their due date.
Class recordings: Video from class meetings, both in Mason Hall and on Zoom, can be seen at the lecture capture page (requires Canvas log in). I'll also archive the Miro whiteboards we use; you'll need to be a member of the class Miro team to see those.
Videos from a more elementary class: I don't know if you'll find these useful, but I recorded lecture videos for all the material in Math 214.

Dates	Topics	Handouts and Lecture Notes	Assigned reading	Assignments
January 6	Review of vectors, matrices	Basics of vectors and matrices Worksheet from Jan 6 Lecture notes for Jan 6
January 11, 13	Review of image, kernel, invertible matrices row operations, row reduced echelon form	Slides for Jan 11 Slides for Jan 13	Skim 1.1, read 1.2-1.6	Problem Set 1 Solution Set 1
January 18, 20	Abstract vector spaces, subspaces, linear independence, spanning, bases, dimension	The axioms of a field Slides for Jan 18 Slides for Jan 20 (edited)	Read 1.1 and 2.1-2.3	Problem Set 2 Solution Set 2
January 25, 27	Coordinates, quotient spaces	Slides for Jan 25 Slides for Jan 27 (up to slide 25)	Read 2.4, 2.6 and appendix A.4	Problem Set 3 Solution Set 3
February 1, 3	Linear transformations, the rank-nullity theorem	Slides for Feb 1 Problems for Feb 3	Read 3.1-3.4	Problem Set 4 Solution Set 4
February 8, 10	Dual vector spaces, transpose	Slides for February 8 Miro for Feb 10	Read 3.5 and 3.7	Exam on February 10. Exam solutions.
February 15, 17	Dual vector spaces, transpose, orthogonal complement	Slides for February 15 Miro for Feb 15 Slides for February 17 Miro for Feb 17"	Reread 3.5 and 3.7	Problem Set 5 Solution Set 5
February 22, 24	Determinants	Slides from February 22 Whiteboard drawing from February 22 Slides from February 24	We'll skip Chapter 4 and come back to it. Read 5.2-5.4	Problem Set 6 Solution Set 6
March 1,3	❄️ ❄️ ❄️ ❄️ ❄️ ❄️ ❄️ ❄️ ❄️ ❄️ ❄️ ❄️	Spring Break!	☀️☀️☀️☀️☀️☀️☀️☀️☀️ ☀️☀️☀️☀️☀️☀️☀️	No assignment
March 8, 10	More on determinants, start eigenvalues and eigenvectors	Problems from March 8 Miro from March 8 Problems from March 10 Miro from March 10	Read 5.6-5.7	Problem Set 7 Solution Set 7
March 15, 17	Characteristic and minimal polynomial, triangularization	Slides from March 15 Slides from March 17 Whiteboard from March 17	Read 6.1-6.4	Problem Set 8 Solution Set 8
March 22, 24	Direct sum decompositions coming from eigenspaces	Slides from March 22 Problems from March 22 and 24 Miro for March 22 and 24 Mathematica notebook from March 24 PDF export of Mathematica notebook from March 24	Read 6.6-6.8	Problem Set 9 Solution Set 9
March 29, 31	Review, start inner products	Whiteboards from March 29 Slides from March 31 Problems from March 31 Miro from March 31		Exam on March 29. Exam solutions.
April 5, 7	Orthonormal bases, orthogonal projection, Gram-Schmidt algorithm	Slides from April 5 Problems from April 7 Miro for April 7 Slides from April 7	Read 8.1-8.4	Problem Set 10 Solution Set 10
April 12, 14	Complex numbers, Hermitian, unitary and normal operators	Slides for April 12 Slides originally meant for April 14, but used on April 12 Miro from April 14 Problems from April 14	Read 8.5	Problem Set 11 Solution Set 11
April 19	Review	Whiteboards for April 19		Final exam 10:30-12:30 Thursday, April 28 Mason Hall 3437