APMA E4008: Advanced Linear Algebra
Course Syllabus, Spring 2023
Course Overview: This is an advanced course on abstract linear algebra. The
emphasis of the course is on the diagonalization of linear operators between ab-
stract vector spaces and their applications. The course contains a detailed and rig-
orous treatment of general vector spaces, linear transforms between vector spaces
and their representations, diagonalization of linear transformations through ma-
trix representation, inner product spaces and the concept of orthogonality, linear
operators on inner product spaces and their singular value decompositions, as well
as some applications of the abstract theory.
Prerequisite: Successful completion of an elementary course on linear algebra
(such as APMA E3101 and APMA E4007 or their equivalent) is required.
Class Time and Location: The class meets Tu Th 8:40AM-9:55AM @ Mudd
633.
Instructor: Yuan He
Email: yh2030@columbia.edu
Office Hours: Tu Th 3:00PM-4:00PM @ 287 Mudd Building.
Teaching Assistant: TBA
Email Policy: Please always include ‘E4008’ in your email subject.
Textbooks:
Linear Algebra (Fourth Edition)
Stephen Friedberg, Arnold Insel and Laurence Spence
ISBN 978-8-1203260-6-4 or 81-203-2606-7
Homework and Exams: There will be 12 - 13 homework sets and each one
is based on 100 points. The lowest score from your homework will be dropped
when calculating your final score. No late homework will be accepted without
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compelling reasons. There will be one midterm exam and one final exam. In
general, no makeup exam will be arranged without compelling reasons.
Grading Policy: The final grade will be weighted roughly as follows:
Homework 20%, Midterm 40%, Final 40%
Course Webpage: All course related documents will be posted on the university
teaching tool, the courseworks system:
http://courseworks.columbia.edu/
Important Dates:
ˆ 01/17, First day of class for E4008
ˆ 03/09, Midterm Exam
ˆ 03/13 - 03/17, Spring Break - No Class
ˆ 04/27, Last day of class for E4008
ˆ 05/05, Final exam for E4008 ( This date is projected by the registrar’s
office based on data available on 12/19/2022)
Academic Dishonesty: Discussions and team works among students are en-
couraged in general. However, the work a student submits for grading, including
homework and exams, must be his/her own work. Students who violate univer-
sity rules on academic dishonesty are subject to disciplinary penalties, including
the possibility of failing the course and/or dismissal from the University. Detailed
information on academic integrity at Columbia University is available here:
http://www.college.columbia.edu/academics/academicintegrity
More explanation on dishonesty in academic work can be found here:
http://www.college.columbia.edu/academics/academicdishonesty
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Students with Disabilities: Columbia University makes every effort to accom-
modate students with disabilities. If you require disability accommodations to
attend the classes or the exams, please contact Columbia Disability Services at
212-854-2388. For more information please visit:
http://health.columbia.edu/content/disability-services
Students with disabilities may be eligible for accommodations related to the ad-
ministration of examinations. Here are more detials:
http://health.columbia.edu/services/testing-accommadations
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Tentative Course Schedule: Here is a tentative plan for the lectures. Changes
of the schedule will be announced in class.
ˆ 01/17 (T): Section 1.1 HW #01 Handout
ˆ 01/19 (R): Section 1.2
ˆ 01/24 (T): Section 1.3 & 1.4 HW #02 Handout
ˆ 01/26 (R): Section 1.5
ˆ 01/31 (T): Section 1.6 HW #03 Handout
ˆ 02/02 (R): Section 2.1 (I)
ˆ 02/07 (T): Section 2.1 (II) HW #04 Handout
ˆ 02/09 (R): Section 2.1 (III)
ˆ 02/14 (T): Section 2.2 (I) HW #05 Handout
ˆ 02/16 (R): Section 2.2 (II)
ˆ 02/21 (T): Section 2.3 HW #06 Handout
ˆ 02/23 (R): Section 2.4
ˆ 02/28 (T): Section 2.5 HW #07 Handout
ˆ 03/02 (R): Section 5.1 (I)
ˆ 03/07 (T): Section 5.1(II)
ˆ 03/09 (R): Midterm
ˆ 03/14 (T): No Class;
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ˆ 03/16 (R): No Class;
ˆ 03/21 (T): Section 5.2(I) HW #08 Handout
ˆ 03/23 (R): Section 5.2(II)
ˆ 03/28 (T): Section 6.1 HW #09 Handout
ˆ 03/30 (R): Section 6.2 (I)
ˆ 04/04 (T): Section 6.2 (II) HW #10 Handout
ˆ 04/06 (R): Section 6.3
ˆ 04/11 (T): Section 6.4 HW #11 Handout
ˆ 04/13 (R): Section 6.5
ˆ 04/18 (T): Section 6.6 (I) HW #12 Handout
ˆ 04/20 (R): Section 6.6(II)
ˆ 04/25 (T): Section 6.7 (I) HW #13 Handout
ˆ 04/27 (R): Section 6.7 (II)
ˆ 05/05 (F) Final Exam 4PM - 6PM