Math 417: Matrix Algebra

Professor: David E Speyer, speyer@umich.edu
Class: 337 Dennison, Monday, Wednesday, Friday 1-2 PM
Office hours: 2844 East Hall, Monday 2-4, Tuesday 10-11, at other times by appointment
Problem Sets due: Wednesdays in class
Textbook: Linear Algebra with Applications, Fourth edition, Otto Bretscher, ISBN 978-0-13-600926-9
Webpage: http://www.math.lsa.umich.edu/~speyer/417.html

Linear algebra is perhaps the most important field of mathematics for computations and applications. Linear problems turn up at every step of every computation and there are well established, powerful methods to solve them. Linear methods are at the heart of computer graphics, every form of data analysis, and is the first approximation to every problem in every field of science. In this course, we will learn the computational methods, the images and the concepts of linear algebra.

Grading: Your final grade will be made out of 25% Midterm 1, 25% Midterm 2, 40% Final Exam and 10% Homework.

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.
Vermeer demonstrates an excellent understanding of perspective. Did he know that it could be described using matrices?
Homework Policy: 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. Homework is due Wednesdays in class. If you cannot turn in your homework at that time, you must contact me in advance to arrange another time.

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.

Exams: The first midterm will take place in class on Monday, October 1. The second midterm will be in class Friday, November 16 9. The final exam will be Thursday, December 20, 1:30-3:30. If you have a medical condition requiring special accomodation during exams, please inform me and provide medical documentation before hand.
Will Hunting realizes that he can count paths through a network using matrices. If you want to learn more about this, take Math 465 or 565.

Syllabus: Readings and problems sets are to be completed before or on the corresponding class date. More details will appear on this calendar as the term progresses.

Date Topics Reading Homework
Sept 5 Introduction to Linear Algebra
Sept 7 Solving linear equations, echelon form Read 1.1 and 1.2
Sept 10 Examples and applications Read 1.3
Sept 12 Matrix operations 1.1 14, 28 and 26
1.2 10, 42 and 43 (Use a calculator for 43)
1.3 4 and 48
Sept 14 Linear maps Read 2.1, additional notes.
Sept 17 Linear maps in geometry Read 2.2
Sept 19 Linear maps and matrices Read 2.3 2.1 8, 12, 26, 28
2.2 20, 32
2.3 6
Sept 21 Inverting matrices Read 2.4
Sept 24 Subspaces Read 3.1
Sept 26 Bases Read 3.2 2.4 2, 4, 40, 41. Explain your answers to 41 in full sentences.
3.1 2, 4, 24, 37 (I'm not sure what the book means by "geometrically", just describe the images and kernels)
Sept 28 Review No mandatory homework, but I encourage you try problems from the practice exam (distributed in class Sept. 26)
Oct 1 MIDTERM 1
Oct 3 Discuss Midterm, intro to dimension Read 3.3 pages 123-126 No homework
Oct 5 Theory underlying bases Finish reading 3.3
Oct 8 Computing bases
Oct 10 Dot products Read 5.1
Optional additional reading: Proof of the Cauchy-Schwartz inequality		 3.3 12, 18, 30 and this problem (Solution)
5.1 6 (use a calculator), 8
Oct 12 Orthonormal bases, orthogonal projection Read 5.3
FALL BREAK Go jump in a leaf pile!
Oct 17 Computing orthonormal bases Read 5.2
Optional additional reading
Oct 19 The method of least squares Read 5.4 NOTE UNUSUAL DUE DATE
5.1 16, 28 (Warning! The vectors in 28 don't have length 1!)
5.2 4, 6, 18, 34
Oct 22 Application: Fourier Series Notes on Fourier series
Oct 24 Catch up 5.3 36, 40
5.4 2, 20, 36
and this problem (Solution)
Oct 26 Introduction to Determinants Reread 2.4 pages 85-86.
Read 6.1 pages 249-252
Oct 29Computing determinants Finish reading 6.1
Oct 31Determinants and row operations Read 6.26.1 2, 4, 6, 12, 22, 26, 40, 44. Show your work; do not simply type the matrices into a computer/calculator.
Nov 2 Determinants multiply Read 6.3 pages 279-283
Nov 5Catch up Finish 6.3
Nov 7 Review Review notes 6.2 2 (use row reduction), 12, 14, 38, 40 and this problem.
Nov 9 MIDTERM 2
Nov 12 Discuss Midterm, start eigenvalues
Nov 14 What is an eigenvalue? Read 7.1, bottom of 299 to middle of 302No homework
Nov 16 Computing eigenvalues and eigenvectorsRead 7.2
Nov 19 Eigenvalues and dynamical systems Read 7.3
Nov 21 Ask me anything mathematical (optional class) If you will not be in class this day, leave the problem set in my mailbox (on the door of East Hall 2844) before class. These problems and 7.1 38, 50
7.2 4, 8, 12
7.3 8, 10, 44
Selected Solutions
THANKSGIVING
Nov 26Eigenvalue examples
Nov 28 DiagonalizationRead 7.4.
These notes were assigned for Friday, but wound up covered on Wednesday.		7.4 2, 4, 6, 32
Nov 30 Complex eigenvaluesRead 7.5
Dec 3 Symmetric matrices and quadratic formsRead 8.1
Dec 5 More on quadratic formsRead 8.2
Optional reading The Spectral Theorem		7.5 20, 32
8.1 4, 24
8.2 2, 21, 22
Solution file for 8.2.22
Dec 7 Applications of eigenvalues of symmetric matrices
Dec 10 REVIEWReview SheetSuggested HW problems to review:
1.1.26,  2.1.28,  3.1.37,  3.3.18,  5.1.28,  5.3.36,  6.1.12,  6.1.40,  6.2.14,  7.1.50,  7.2.12,  7.3.8,  7.4.4,  8.1.4,  8.2.22
Dec 13, 2-4 PM Review session, East Hall 2866
Dec 19, 3-5 PM Review session, East Hall 3096
Dec 20 FINAL EXAM (in our classroom) 1:30-3:30 PM