MATH 2R03 is a second course in linear algebra. From the calendar:
Comparison to Math 2LA3:
This course's primary concern will be the theory of linear algebra. Math 2LA3 focuses more on the applications of linear algebra, and is offered in both terms. At least one (you can take both) of Math 2LA3 or Math 2R03 is required for all Honours Math and Stats programmes. Math 2R03 is required for Honours Math and Stats with a Mathematics subplan. Either linear algebra course is an allowable prerequisite for most third year Math and Stats courses. For Math 3A03, Math 3B03, Math 3GR3, Math 3F03, Math 3FF3 and Math 3QC3, the requirement is Math 2R03 or a grade of at least a B in 2LA3 (starting in 202223).

Important Note:
The purpose of this webpage is to collect together all of the needed resources for the course.
Instructor:
Office: Hamilton Hall 419
Office Hours: Fridays 12PM
Email: vantuyl@math.mcmaster.ca
TA:
Jananan (Jan) Arulseelan
Email:arulseej@mcmaster.ca
Place and Time:
This course will be offered inperson (online for first four weeks)
Class C01: Tuesday, Thursday, Friday 2:303:20 Burke Science Building (BSB) B135
Tutorial T01: Friday 3:304:20 ABB 271
Tutorial T02: Wednesday 3:304:20 PGCLL M12
Textbook:
Linear Algebra Done Right
by Sheldon Axler
This book can be download for free from the McMaster Library.
Here is a link to the book on the campus bookstore website: Purchase at Campus Bookstore
Important Links:
The following online resources will be used during this course:
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We will be using the following schedule. Please note that there may be changes; please refer back to this page often to stay uptodate.
Course Delivery:
The course and its tutorials will be delivered online until February 7, and then inperson. Until February 7, the online portion of the course will be delivered using both asynchronous and synchronous components. The asynchronous component consist of video lectures of the course material (posted on Avenue and YouTube). For the synchronous component, we will use the scheduled class time as follows:
A detailed schedule is given below.
Math 2R03 Schedule  

Week 1 (Jan 1014)  
Homework: Assignment 0 (Due Jan 15)  
Lecture  Topic  Video 
Lecture 1  1.A R^n and and C^n  Video 
Lecture 2  1.B Vector Spaces  Video 
Lecture 3  1.C Subspaces I  Video 
Week 2 (Jan 1721)  
Homework: Assignment 1 (Due Jan 22)  
Lecture 4  1.C Subspaces II Writing Proofs 
Video 
Lecture 5  2.A Span and Linear Independence I 
Video 
Lecture 6  2.A Span and Linear Independence II  Video 
Week 3 (Jan 2428)  
Homework: Assignment 2 (Due Jan 29)  
Lecture 7  2.B Bases  Video 
Lecture 8  2.C Dimension  Video 
Lecture 9  3.A Vector Space of Linear Maps  Video 
Week 4 (Jan 31Feb 4)  
Homework: Assignment 3 (Due Feb 5)  
Lecture 10  3.B Null Spaces and Ranges I  Video 
Lecture 11  3.B Null Spaces and Ranges II 3.C Matrices 
Video 
Lecture 12  3.D Invertibility and Isomorphic Vector Spaces I 
Video 
Week 5 (Feb 711)  
Homework: Study for Midterm 1 (Feb 11)  
Lecture 13  3.D Invertibility and Isomorphic Vector Spaces II 
Video 
Lecture 14  4 Polynomials  Video 
Lecture 15  Midterm 1 (Feb. 11)  
Week 6 (Feb 1418)  
Homework: Assignment 4 (Due Feb 26) Note Date  
Lecture 16  5.A Invariant Subspaces I  Video 
Lecture 17  5.A Invariant Subspaces II 5.B Eigenvectors and UpperTriangular Matrices I 
Video 
Lecture 18 
5.B Eigenvectors and UpperTriangular Matrics II 
Video 
Week 7 (Feb 21  25)  
Reading Week (No Classes)  
Week 8 (Feb 28March 4)  
Homework: Assignment 5 (Due March 5)  
Lecture 19  5.C Eigenspaces and Diagonal Matrices  Video 
Lecture 20  8.A Generalized Eigenvectors and Nilpotent Operators I 
Video 
Lecture 21  8.A Generalized Eigenvectors and Nilpotent Operators II 
Video 
Week 9 (March 711)  
Homework: Assignment 6 (Due March 12)  
Lecture 22  8.B Decomposition of an Operator I  Video 
Lecture 23  8.B Decomposition of an Operator II  Video 
Lecture 24 
8.C Characteristic and Minimal Polynomials 
Video 
Week 10 (March 1418)  
Homework: Study for Midterm 2 (March 18)  
Lecture 25  8.D Jordan Form  Video Extra Video 
Lecture 26  6.A Inner Products and Norms I  Video 
Lecture 27  Midterm II (March 18)  
Week 11 (March 2125)  
Homework: Assignment 7 (March 26)  
Lecture 28  6.A Inner Products and Norms II  Video 
Lecture 29 
6.B Orthonormal Bases  Video 
Lecture 30  6.B Linear Functionals  Video 
Week 12 (March 28April 1)  
Homework: Assignment 8 (April 2)  
Lecture 31  7.A SelfAdjoint and Normal Operators I  Video 
Lecture 32  7.A SelfAdjoint and Normal Operators II  Video 
Lecture 33  7.B The Spectral Theorem  Video 
Week 13 (April 48)  
Homework: (Nothing due this week)  
Lecture 34  7.C Positive Operators and Isometries  Video 
Lecture 35  7.D Polar Decompositions  Video 
Lecture 36  7.D Singular Value Decomposition  Video 
Week 14 (April 1112)  
Homework: Assignment 9 (Due April 12)  
Lecture 37  Buffer/Review 
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There will be nine homework assignments (your lowest mark will be dropped). Assignments are posted below. Assignments will be submitted via Crowdmark. You will receive an email to your McMaster account that you will use to upload your assignment. All assignments due by 11:59PM on the due date.
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All class handouts are available as PDF files (except where indicated)
Course Information
Course handout from first day of class
Midterm 1 Review Sheet
Handout describing first midterm.
Midterm 2 Review Sheet
Handout describing second midterm.
Exam Review Sheet
Handout describing final exam.
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Weighting 1
20% = 9 Assignments (best 8 used)
40% = Midterms (2 x 20%)
40% = Final Exam
Weighting 2
20% = 9 Assignments (best 8 used)
20% = Maximum of Midterm 1 and 2
60% = Final Exam
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2. Inclusivity and a Culture of Respect. As a McMaster student, you have the right to experience and the responsibility to demonstrate respectful and dignified interactions within all of our living, learning and working communities. Expectations are described in Code of Student Rights and Responsibilities
It is essential that students be mindful of their interactions online, as the Code remains in effect in virtual learning environments. The Code applies to any interactions that adversely affect, disrupt, or interfere with reasonable participation in University activities. Student disruptions or behaviours that interfere with university functions on online platforms (e.g. use of Avenue 2 Learn, WebEx or Zoom for delivery), will be taken very seriously and will be investigated. Outcomes may include restriction or removal of the involved students' access to these platforms. Additional information about the Code and netiquette can be found here.
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Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: Grade of F assigned for academic dishonesty), and/or suspension or expulsion from the university.
It is your responsibility to understand what constitutes academic
dishonesty. For information on the various types of academic
dishonesty
please refer to the Academic Integrity Policy, located at:
http://www.mcmaster.ca/academicintegrity/
The following illustrates only three forms of academic dishonesty:
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5. Requests for Relief for Missed Academic Term Work. If you have missed work, it is your responsibility to take action. If you are absent from the university for medical and nonmedical (personal) situations, lasting fewer than 3 days, you may report your absence, once per term, without documentation, using the McMaster Student Absence Form (MSAF). See Requests for Relief for Missed Academic Term Work
Absences for a longer duration or for other reasons must be reported to your Faculty/Program office, with documentation, and relief from term work may not necessarily be granted. In Math 2R03, the percentages of the missed work will be transferred to the final examination. Please note that the MSAF may not be used for term work worth 25% or more, nor can it be used for the final examination.
6. Academic Accommodation for Religious, Indigenous or Spiritual Observances (RISO). Students requiring academic accommodation based on religious, indigenous or spiritual observances should follow the procedures set out in the RISO policy. Students requiring a RISO accommodation should submit their request to their Faculty Office normally within 10 working days of the beginning of term in which they anticipate a need for accommodation or to the Registrar's Office prior to their examinations. Students should also contact their instructors as soon as possible to make alternative arrangements for classes, assignments, and tests.
7. Important Message. The instructor and university reserve the right to modify elements of the course during the term. The University reserves the right to change the dates and deadlines for any or all courses in extreme circumstances (e.g., severe weather, labour disruptions, etc.). Changes will be communicated through regular McMaster communication channels, such as McMaster Daily News, A2L and/or McMaster email. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.
8. Online Statement for Courses Requiring Online Access or Work. In this course we will be using Zoom, AvenuetoLearn, YouTube, and Crowdmark. Students should be aware that, when they access the electronic components of this course, private information such as first and last names, user names for the McMaster email accounts, and program affiliation may become apparent to all other students in the same course. The available information is dependent on the technology used. Continuation in this course will be deemed consent to this disclosure. If you have any questions or concerns about such disclosure please discuss this with the course instructor.
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