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 2022-23).
The purpose of this webpage is to collect together all of the needed resources for the course.
Office: Hamilton Hall 419
Office Hours: Fridays 1-2PM
Jananan (Jan) Arulseelan
Place and Time:
This course will be offered in-person (online for first four weeks)
Class C01: Tuesday, Thursday, Friday 2:30-3:20 Burke Science Building (BSB) B135
Tutorial T01: Friday 3:30-4:20 ABB 271
Tutorial T02: Wednesday 3:30-4:20 PGCLL M12
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
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 up-to-date.
The course and its tutorials will be delivered online until February 7, and then in-person. 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 10-14)|
|Homework: Assignment 0 (Due Jan 15)|
|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 17-21)|
|Homework: Assignment 1 (Due Jan 22)|
|Lecture 4||1.C Subspaces II
|Lecture 5||2.A Span and Linear
|Lecture 6||2.A Span and Linear Independence II||Video|
|Week 3 (Jan 24-28)|
|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 31-Feb 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
|Lecture 12||3.D Invertibility and Isomorphic Vector
|Week 5 (Feb 7-11)|
|Homework: Study for Midterm 1 (Feb 11)|
|Lecture 13||3.D Invertibility and Isomorphic Vector
|Lecture 14||4 Polynomials||Video|
|Lecture 15||Midterm 1 (Feb. 11)|
|Week 6 (Feb 14-18)|
|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 Upper-Triangular
||5.B Eigenvectors and Upper-Triangular
|Week 7 (Feb 21 - 25)|
|Reading Week (No Classes)|
|Week 8 (Feb 28-March 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
|Lecture 21||8.A Generalized Eigenvectors and
Nilpotent Operators II
|Week 9 (March 7-11)|
|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|
||8.C Characteristic and Minimal
|Week 10 (March 14-18)|
|Homework: Study for Midterm 2 (March 18)|
|Lecture 25||8.D Jordan Form||Video
|Lecture 26||6.A Inner Products and Norms I||Video|
|Lecture 27||Midterm II (March 18)|
|Week 11 (March 21-25)|
|Homework: Assignment 7 (March 26)|
|Lecture 28||6.A Inner Products and Norms II||Video|
||6.B Orthonormal Bases||Video|
|Lecture 30||6.B Linear Functionals||Video|
|Week 12 (March 28-April 1)|
|Homework: Assignment 8 (April 2)|
|Lecture 31||7.A Self-Adjoint and Normal Operators I||Video|
|Lecture 32||7.A Self-Adjoint and Normal Operators II||Video|
|Lecture 33||7.B The Spectral Theorem||Video|
|Week 13 (April 4-8)|
|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 11-12)|
|Homework: Assignment 9 (Due April 12)|
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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 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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20% = 9 Assignments (best 8 used)
40% = Midterms (2 x 20%)
40% = Final Exam
20% = 9 Assignments (best 8 used)
20% = Maximum of Midterm 1 and 2
60% = Final Exam
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please refer to the Academic Integrity Policy, located at:
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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 non-medical (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.
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8. On-line Statement for Courses Requiring Online Access or Work. In this course we will be using Zoom, Avenue-to-Learn, 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 e-mail 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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