arminstraub.com - Spring 2021: Linear Algebra II (Math 316)

Overview

Instructor	Dr. Armin Straub MSPB 313 straub@southalabama.edu (251) 460-7262 (please use e-mail whenever possible)
Office hours	MWF, 9-11am, or by appointment Held virtually using Zoom; please make an appointment by email at least 2 hours in advance.
Class schedule	MWF, 8:00-8:55am, in MSPB 410 Due to COVID restrictions, you may only attend those meetings assigned to the cohort you signed up for.
Midterm exams	The tentative dates for our two midterm exams are: Friday, February 26 Monday, April 5
Final exam	Monday, May 3 — 8:00-10:00am
Online grades	Homework Scores Exams: USAonline (Canvas)
Syllabus	syllabus.pdf

Assignments and course material

In order to be able to view the lecture recordings, you need to be logged into USAonline (Canvas). If you are still running into access issues, then please view the recordings through Panopto Video in our course page on Canvas.

	Dates	Assignments and course material
#1	01/20 01/22 01/25	Assignments: Homework Set 1 (due 2/1) Lecture notes: lectures-01-03.pdf Lecture recordings: lecture01-1-linear-algebra.mp4 (corresponding PDF) lecture01-2-linear-algebra-part2.mp4 (corresponding PDF) lecture02-1-gaussian-elimination.mp4 (corresponding PDF) lecture02-2-lu-decomposition.mp4 (corresponding PDF) lecture03-null-space.mp4 (corresponding PDF) Class schedule: 01/20: online using pre-recorded lectures 01/22: in-person meeting 01/25: online using pre-recorded lectures
#2	01/27 01/29 02/01	Assignments: Homework Set 2 (due 2/8) Lecture notes: lectures-04-06.pdf Lecture recordings: lecture04-1-review-determinants.mp4 (corresponding PDF) lecture04-2-review-eigenvectors.mp4 (corresponding PDF) lecture04-3-diagonalization.mp4 (corresponding PDF) lecture05-1-orthogonality.mp4 (corresponding PDF) lecture05-2-orthogonal-complements.mp4 (corresponding PDF) lecture06-fundamental-theorem.mp4 (corresponding PDF) Class schedule: 01/27: in-person meeting 01/29: in-person meeting 02/01: online using pre-recorded lectures
#3	02/03 02/05 02/08	Assignments: Homework Set 3 (due 2/15) Lecture notes: lectures-07-09.pdf Lecture recordings: lecture07-1-consistency.mp4 (corresponding PDF) lecture07-2-least-squares.mp4 (corresponding PDF) lecture08-least-squares-lines.mp4 (corresponding PDF) lecture09-1-least-squares-data-fitting.mp4 (corresponding PDF) lecture09-2-orthogonal-projections.mp4 (corresponding PDF) Class schedule: 02/03: in-person meeting 02/05: in-person meeting 02/08: online using pre-recorded lectures
#4	02/10 02/12 02/15	Assignments: Homework Set 4 (due 2/22) Lecture notes: lectures-10-12.pdf Lecture recordings: lecture10-projection-matrices.mp4 (corresponding PDF) lecture11-1-orthogonal-bases.mp4 (corresponding PDF) lecture11-2-orthogonal-bases-examples.mp4 (corresponding PDF) lecture12-gram-schmidt.mp4 (corresponding PDF) Class schedule: 02/10: in-person meeting 02/12: in-person meeting 02/15: online using pre-recorded lectures
#5	02/17 02/19 02/22 02/24	Assignments: Homework Set 5 (due 2/26) Lecture notes: lectures-13-15.pdf Lecture recordings: lecture13-qr-decomposition.mp4 (corresponding PDF) lecture14-1-orthogonal-matrices.mp4 (corresponding PDF) lecture14-2-diagonalizability.mp4 (corresponding PDF) lecture15-spectral-theorem.mp4 (corresponding PDF) Class schedule: 02/17: in-person meeting 02/19: in-person meeting 02/22: online using pre-recorded lectures 02/24: online via Zoom zoom-02-24.mp4 (corresponding PDF)
	lectures-01-15.pdf (all lecture notes up to now in one big file)
	02/26	Midterm Exam #1 Practice material: midterm01-practice.pdf midterm01-practice-solution.pdf Format of the exam: Not the real Midterm #1
#6	03/01 03/03 03/05	Assignments: Homework Set 6 (due 3/14) Lecture notes: lectures-16-18.pdf Lecture recordings: lecture16-powers-of-matrices.mp4 (corresponding PDF) lecture17-markov-chains.mp4 (corresponding PDF) lecture18-pagerank-algorithm.mp4 (corresponding PDF) Class schedule: 03/01: online using pre-recorded lectures 03/03: in-person meeting 03/05: in-person meeting
#7	03/08 03/10 03/12 03/15	Assignments: Homework Set 7 (due 3/22) Lecture notes: lectures-19-21.pdf Lecture recordings: lecture19-recurrence-equations.mp4 (corresponding PDF) lecture20-solving-recurrences.mp4 (corresponding PDF) lecture21-projection-matrices-again.mp4 (corresponding PDF) Class schedule: 03/08: online using pre-recorded lectures 03/10: student holiday 03/12: in-person meeting 03/15: online using pre-recorded lectures
#8	03/17 03/19 03/22	Assignments: Homework Set 8 (due 3/29) homework08-example-problems.pdf Lecture notes: lectures-22-24.pdf Lecture recordings: lecture22-reflections.mp4 (corresponding PDF) lecture22-exponential.mp4 (corresponding PDF) lecture23-1-systems-of-diffeqs.mp4 (corresponding PDF) lecture23-2-solving-system-of-diffeqs.mp4 (corresponding PDF) lecture24-de-to-system.mp4 (corresponding PDF) lecture24-jnf-1.mp4 (corresponding PDF) Class schedule: 03/17: in-person meeting 03/19: in-person meeting 03/22: online using pre-recorded lectures
#9	03/24 03/26 03/29 03/31 04/02	Assignments: Homework Set 9 (due 4/4) homework09-example-problems.pdf Lecture notes: lectures-25-28.pdf Lecture recordings: lecture25-jnf-2.mp4 (corresponding PDF) lecture25-jnf-3.mp4 (corresponding PDF) lecture26-de-jnf.mp4 (corresponding PDF) lecture27-rotations.mp4 (corresponding PDF) lecture27-complex.mp4 (corresponding PDF) Class schedule: 03/24: in-person meeting 03/26: in-person meeting 03/29: online using pre-recorded lectures 03/31: in-person meeting 04/02: online via Zoom zoom-04-02.mp4 (corresponding PDF)
	lectures-16-28.pdf (all lecture notes since the previous exam in one big file)
	04/05	Midterm Exam #2 Practice material: midterm02-practice.pdf midterm02-practice-solution.pdf
#10	04/07 04/09 04/12	Assignments: Homework Set 10 (due 4/19) homework10-example-problems.pdf Lecture notes: lectures-29-31.pdf Lecture recordings: lecture29-svd-intro.mp4 (corresponding PDF) lecture30-svd-example.mp4 (corresponding PDF) Eigenvectors and eigenvalues - 3blue1brown We Recommend a Singular Value Decomposition - David Austin Class schedule: 04/07: in-person meeting 04/09: in-person meeting 04/12: online using pre-recorded lectures
#11	04/14 04/16 04/19	Assignments: Homework Set 11 (due 4/26) homework11-example-problems.pdf Lecture notes: lectures-32-34.pdf Lecture recordings: lecture32-pseudoinverse-1.mp4 (corresponding PDF) lecture32-pseudoinverse-2.mp4 (corresponding PDF) lecture33-matrix-approximation.mp4 (corresponding PDF) lecture34-function-spaces.mp4 (corresponding PDF) Class schedule: 04/14: in-person meeting 04/16: in-person meeting 04/19: online using pre-recorded lectures
#12	04/21 04/23 04/26 04/28 04/30	Assignments: Homework Set 12 (due 4/30) homework12-example-problems.pdf Lecture notes: lectures-35-38.pdf Lecture recordings: lecture35-function-approximation.mp4 (corresponding PDF) lecture37-fourier-series.mp4 (corresponding PDF) Class schedule: 04/21: in-person meeting 04/23: in-person meeting 04/26: online using pre-recorded lectures 04/28: in-person meeting 04/30: online via Zoom zoom-04-30.mp4 (corresponding PDF)
	lectures-29-38.pdf (all lecture notes since the previous exam in one big file)
	05/03	Final Exam Practice material: final-practice.pdf final-practice-solution.pdf

About the homework

Homework problems are posted for each unit. Homework is submitted online, and you have an unlimited number of attempts. Only the best score is used for your grade.
Most problems have a random component (which allows you to continue practicing throughout the semester without putting your scores at risk).
Aim to complete the problems well before the posted due date.
A 15% penalty applies if homework is submitted late.
Collect a bonus point for each mathematical typo you find in the lecture notes (that is not yet fixed online), or by reporting mistakes in the homework system. Each bonus point is worth 1% towards a midterm exam.
The homework system is written by myself in the hope that you find it beneficial. Please help make it as useful as possible by letting me know about any issues!

Sage

As part of this course, we will explore the open-source free computer algebra system Sage to assist with more involved calculations.

If you just want to run a handful quick computations (without saving your work), you can use the text box below.

A convenient way to use Sage more seriously is https://cocalc.com. This free cloud service does not require you to install anything, and you can access your files and computations from any computer as long as you have internet. To do computations, once you are logged in and inside a project, you will need to create a "Sage notebook" as a new file.

Here are some other things to try:

Sage makes solving least squares problems pleasant. For instance, to solve Example 45 in Lecture 8:

A = matrix([[1,2],[1,5],[1,7],[1,8]]); b = vector([1,2,3,3])
(A.transpose()*A).solve_right(A.transpose()*b)

Sage can compute QR decompositions. For instance, we can have it do Example 70 in Lecture 13 for us:
```
A = matrix(QQbar, [[0,2,1],[3,1,1],[0,0,1],[0,0,1]])
A.QR(full=false)
```
The result is a tuple of the two matrices Q and R. If that is too much at once, A.QR(full=false)[0] will produce Q, and A.QR(full=false)[1] will produce R. (Can you figure out what happens if you omit the full=false? Check out the comment under "Variations" for the QR decomposition in the lecture sketch. On the other hand, the QQbar is telling Sage to compute with algebraic numbers (instead of just rational numbers); if omitted, it would complain that square roots are not available.)