MATH2048 - Honours Linear Algebra II - 2023/24
Announcement
- 2022-23 Midterm 2 is posted for reference.
- 2022-23 Midterm 1 is posted for reference.
- Due date of HW4 is postponed to 2023-10-09; Due date of HW5 is postponed to 2023-10-16
Submission of homework assignments
- Log onto https://blackboard.cuhk.edu.hk/ and click on our course 2023R1 Honours Linear Algebra II (MATH2048). Click on "course contents" and click on "Homework X (Due...)". Follow the instructions therein to upload your solution. An illustration can be downloaded here.
- Please scan your written solution into a single pdf file and save it with the name like: YourStudentID_HW1.pdf. There are several useful apps for you to take a picture of your solution and scan your document (such as CamScanner HD and Microsoft Lens).
- Homework 1 has been posted. It will be due on September 15 before 1159PM. Please submit your homework via Blackboard.
- There will be no tutorial in the first week.
General Information
Lecturer
-
Prof. Ronald Lok Ming LUI
- Office: LSB 207
- Tel: 3943-7975
- Email:
Teaching Assistant
-
Li Zhiwen
- Office: LSB 222A
- Tel: 3943 3575
- Email:
-
Shen Jianhao
- Office: 505 AB1
- Tel: 3943 4298
- Email:
Time and Venue
- Lecture: Mo 3:30PM - 5:15PM (Wu Ho Man Yuen Bldg 406); Th 5:30PM - 6:15PM (Y.C. Liang Hall G04)
- Tutorial: Th 4:30PM - 5:15PM (Y.C. Liang Hall G04)
Course Description
This course is a continuation of Honoured Linear Algebra I (MATH 1038). It is a second course on linear algebra and will cover basic concepts of abstract vector spaces over general field, direct sum, direct product, quotient spaces, existence of basis by Zorn's lemma, linear transformations, dual spaces, eigenvalues and eigenvectors, diagonalizability, operators on inner product spaces, orthogonality and Gram-Schmidt process, adjoint, normal and self-adjoint operators, spectral theorems, bilinear form and Jordan canonical forms. More emphasis will be put on the theoretical understanding of basic concepts in linear algebra.
Textbooks
- Friedberg, Insel and Spence, Linear algebra, 4th edition, Pearson.
Lecture Notes
- Lecture 1: Revision of Math1030/1038
- Lecture 2: Direct Sum
- Lecture 3: Direct Product and Quotient Space
- Lecture 4: Existence of basis by Zorn's lemma
- Lecture 5: More about Zorn's lemma and Intro to linear transformation
- Lecture 6: Applications of Rank-Nullity Theorem, Matrix representation of linear transformation
- Lecture 7: More about matrix representation, isomorphism
- Lecture 8: More about isomorphism
- Lecture 9: Space of linear transformation, change of coordinates
- Lecture 10: Dual spaces, transpose of linear transformation
- Lecture 11: Eigenvalues and Eigenvectors
- Lecture 12: Necessary and sufficient condition for diagonalizability
- Lecture 13: Examples of diagonalizability, T-invariant subspaces
- Lecture 14: More about T-invariant subspaces, inner product space
- Lecture 15: Orthogonal/Orthonormal set, proof of G-S process
- Lecture 16: Orthogonal Complement, Adjoint of a linear operator
- Lecture 17: Properties of Adjoint, Normal linear operator, Existence of o.n. basis of eigenvectors
- Lecture 18: Unitary and self-adjoint linear operator
- Lecture 19: Spectral decomposition theorem
- Lecture 20: Jordan Canonical Decomposition (Part I)
- Lecture 21: Jordan Canonical Decomposition (Part II)
Tutorial Notes
- Tutorial Note 1
- Tutorial Note 2
- Tutorial Note 3
- Tutorial Note 4
- Tutorial Note 5
- Tutorial Note 6
- Tutorial Note 7
- Tutorial Note 8
Assignments
- Homework 1 (Due on 2023-09-15 before 1159PM)
- Homework 2 (Due on 2023-09-22 before 1159PM)
- Homework 3 (Due on 2023-09-29 before 1159PM)
- Homework 4 (Updated 231005) (Due on 2023-10-09 before 1159PM)
- Homework 5 (Updated 231005) (Due on 2023-10-16 before 1159PM)
- Homework 6 (Due on 2023-10-30 before 1159PM)
- Homework 7 (Due on 2023-11-06 before 1159PM)
- Homework 8 (Due on 2023-11-13 before 1159PM)
- Homework 9 (Due on 2023-11-27 before 1159PM)
- Homework 10 (Due on 2023-12-04before 1159PM)
Quizzes and Exams
Solutions
- HW1 Solution
- HW2 Solution
- HW3 Solution
- HW4 Solution
- HW5 Solution
- Midterm 1 Solution
- HW6 Solution (Q5 Updated on 231113)
- HW7 Solution
- HW8 Solution
- Midterm 2 Solution
- HW9 Solution
- HW10 Solution
Assessment Scheme
| Homework | 10% | |
| Midterm 1 (October 19, 4:30pm-6:15pm) | 20% | |
| Midterm 2 (November 16, 4:30pm-6:15pm) | 20% | |
| Final | 50% |
Honesty in Academic Work
The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: December 02, 2023 07:08:15