MATH 2LA3
Applications of Linear Algebra
Fall 2022


Announcements:

Course Information:


Assignments:


There will be 6 assignments this semester.  Your lowest assignment score will be droped when computing your assignment average in the course. Assignments are worth 10% of your final grade in this course, so each assignment will be worth 2% of your final grade (not counting your lowest assignment grade).  Assignments are conducted online through childsmath.  You can access them by clicking on the following link and following the posted instructions:  https://www.childsmath.ca/childsa/forms/main_login.php

The assignment due dates (tentative) are as follows:

  1. Assignment #1 is due on Tuesday, September 20 by 11:59pm.
  2. Assignment #2 is due on Tuesday, October 4 by 11:59pm.
  3. Assignment #3 is due on Tuesday, October 25 by 11:59pm.
  4. Assignment #4 is due on Tuesday, November 8 by 11:59pm.
  5. Assignment #5 is due on Tuesday, November 22 by 11:59pm.
  6. Assignment #6 is due on Tuesday, December 6 by 11:59pm.

 

Test Dates:

There will be three 50-minute tests held in person on October 6, November 3, and November 24 (tentative dates) during the scheduled class time. Further details on the tests will be given in class and announced on the course web page. The McMaster standard calculator is allowed on all tests. 

Final Exam Information:

A final exam for this courses will be scheduled by the registrar.  Details will be posted on the course website as they become available.

Lecture Schedule (tentative):

Lecture schedule for Math 2LA3 (tentative)

The following lecture schedule is tentative and could change as the term proceeds.  The chapter and section information are relative to the 6th edition of Linear Algebra and Its Applications by Lay, Lay and McDonald.

A more detailed, lecture by lecture schedule can be found below this list.

Week 1, September 6-9

        Review from Math 1B3 (Chapters 1, 2, and 4)

        Practice Problems: Section 2.8 #11, 13, 18, 19, 20, 31, 33, 45 (use WolframAlpha or some other software); section 2.9, #9, 13.

Week 2, September 12-16

        Continuation of Review.
         
        Practice problems: 4.1, #11, 13, 43 (don't do this by hand); 4.2 #5, 49 (use technology); 4.3 #15, 17; 4.4, #3, 7, 39 (not by hand); 4.5, #9, 11, 13, 53 (use tech)

Week 3, September 19-23

         Introduction to linear programming (Chapter 9, sections 2, 3), Optimization problems.

         Practice problems:  Section 9.2: #1, 3, 5, use desmos to solve 7, 9, 15, 16, 17

Week 4, September 26-30

        Optimization problems continued (Section 9.3)

        Practice problems:  Section 9.3: #1, 3, 5, 13, 15, 16  (do some of these by hand, and some using Wolfram Alpha, Matlab, or some other software)

Week 5, October 3-7  (test 1, October 6, in class)

         Review of eigenvalues and eigenvectors; Chapter 5 sections 1 - 3

         Practice problemsSection 5.1, #13, 15, 45, 47 (for 45, 47 - use WolframAlpha or equivalent), 5.2: 9, 11, 35 , 5.3: 17, 19, 41 (with any available tech)

Week 6, October 10-14

        
Reading week, no classes

Week 7, October 17-21

        Review, continued, orthogonality;  Chapter 6, sections 1- 3      

Week 8, October 24-28

       
Gram-Schmidt, QR decomposition, projection matrices, Least-squares; Chapter 6, sections 4, 5

         Practice problems: Section 6.1:  1-18; Section 6.2: 1-10, 13, 15, 21, 22; Section 6.3: 1, 5, 9, 17; Section 6.4: 1, 3, 5, 9, 11  13,  15

Week 9, October 31-November 4 (test 2, November 3, in class)

       
Least-squares, Orthogonal diagonalization; Chapter 6, sections 5, 6, Chapter 7, section 7.1

        Practice problems: Section 6.5: 2 - 6, 9-11, 15  Section 7.1: 13-22

         Added:  Section 6.6:1-4, Section 7.1: 39, 40

Week 10, November 7-11

        The spectral theorem, quadratic forms. Chapter 7, sections 1 and 2

        Practice problems: Section 7.2: 9-20


Week 11, November 14-18

         Constrained Optimization Singular value decomposition (SVD); Chapter 7, sections 3 and 4

         Section 7.4: 1-16, 26-29 (use Wolfram Alpha or other software).

         Added:  Section 7.3:1, 3 (a), (b), 7, 9, 11


Week 12, November 21-25 (test #3, November 24, in class)

        SVD
  


Week 13, November 28-December 2

        SVD, Principal component analysis

      Practice problems: Section 7.5: 1, 2, 7

Week 14, December 5-8

        SVD applications, course wrap-up




Tentative Lecture by Lecture schedule (will be updated on a regular basis)

Lecture #

Date

topics covered

reading/resources/comments

1

7/09/22

course introduction, the vector space R^n

Invertible Matrix Theorem
Lecture #1 notes
Introduction, Section 1.3

2

8/09/22

 matrices, matrix multiplication, subspaces of R^n

Sections 1.3, 1.7, 2.1, 2.8 of the textbook

Lecture #2 notes

3

12/09/22

bases, rank,  reduced row echelon form

Sections 1.2, 2.8, 2.9

Lecture #3 notes

4

14/09/22

finding, extending a basis for a subspace.
Basis for a null space.

Sections  2.3, 2.8, 2.9, 4.2, 4.3, 4.4, 4.5

Lecture #4 notes

5

15/09/22

 invertible matrices, introduction to linear programming

Sections  3.2, 4.5, 9.2

Lecture #5 notes

6

19/09/22

geometric method for solving linear programming problems

Section 9.2

Desmos Graphing Website

Lecture #6 notes

7

21/09/22

continued, the simplex method, introduction

Sections 9.2, 9.3

3-d graphing website

Lecture #7 notes

8

22/09/22

 continued

Sections 9.2, 9.3

Lecture #8 notes

9

26/09/22 the simplex method Section 9.3
Lecture #9 notes
Simplex Method Example from the lecture

10

28/09/22 continued Section 9.3
Lecture #10 notes

11

29/09/22 continued, review of eigenvalues, eigenvectors Sections 9.3, 5.1, 5.2
Lecture #11 notes

12

3/10/22 review of eigenvalues, eigenvectors Sections 5.1, 5.2
Lecture #12 notes

13

5/10/22 similarity and diagonalizability
Sections 5.2, 5.3
Lecture #13 notes

14

6/10/22 midterm test #1

15

17/10/22 continued, diagonalization Sections 5.1, 5.2, 5.3
Lecture #15 notes

16

19/10/22 orthogonality, orthogonal complement Sections 6.1,  6.2
Lecture #16 notes

17

20/10/22 orthogonal and orthonormal bases, orthogonal projections Sections 6.2, 6.3
Lecture #17 notes

18

24/10/22 orthogonal projections, Gram-Schmidt Process Sections 6.3, 6.4
Lecture #18 notes

19

26/10/22 Gram-Schmidt Process, QR decomposition Section 6.4
Lecture #19 notes

20

27/10/22 QR factorization, projection matrices Sections 6.4, 6.5
Lecture #20 notes

21

31/10/22 least-squares Section 6.5
Lecture #21 notes

22

2/11/22 least-squares Section 6.5
Lecture #22 notes

23

3/11/22 midterm test #2

24

7/11/22 symmetric matrices Section 7.1
Lecture #24 notes

25

9/11/22 symmetric matrices Section 7.1
Lecture #25 notes

26

10/11/22 quadratic forms Section 7.2
Lecture #26 notes

27

14/11/22 quadratic forms Sections 7.2, 7.3
Lecture #27 notes

28

16/11/22 constrained optimization Section 7.3
Lecture #28 notes

29

17/11/22 SVD Section 7.4
Lecture #29 notes

30

21/11/22 SVD Section 7.4
Lecture #30 notes

31

23/11/22 SVD Section 7.4
Lecture #31 notes

32

24/11/22 midterm test #3

33

28/11/22 SVD Section 7.4
Lecture #33 notes

34

30/11/22 Principal Component Analysis Section 7.5
Lecture #34 notes

35

1/12/22 Principal Component Analysis Section 7.5
Lecture #35 notes

36

5/12/22 image compression Image compression demo
Lecture #36 notes
37 7/12/22 facial recognition Eigenfaces example
Faces DataSet
Face recognition
Eigenfaces
Lecture #37 notes
38 8/12/22 course wrap up, review Lecture #38 notes

 





Matt Valeriote