MATH2048  Honours Linear Algebra II  2023/24
Announcement
 202223 Midterm 2 is posted for reference.
 202223 Midterm 1 is posted for reference.
 Due date of HW4 is postponed to 20231009; Due date of HW5 is postponed to 20231016
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: 39437975
 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 GramSchmidt process, adjoint, normal and selfadjoint 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 RankNullity 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, Tinvariant subspaces
 Lecture 14: More about Tinvariant subspaces, inner product space
 Lecture 15: Orthogonal/Orthonormal set, proof of GS 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 selfadjoint 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 20230915 before 1159PM)
 Homework 2 (Due on 20230922 before 1159PM)
 Homework 3 (Due on 20230929 before 1159PM)
 Homework 4 (Updated 231005) (Due on 20231009 before 1159PM)
 Homework 5 (Updated 231005) (Due on 20231016 before 1159PM)
 Homework 6 (Due on 20231030 before 1159PM)
 Homework 7 (Due on 20231106 before 1159PM)
 Homework 8 (Due on 20231113 before 1159PM)
 Homework 9 (Due on 20231127 before 1159PM)
 Homework 10 (Due on 20231204before 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, 4:30pm6:15pm)  20%  
Midterm 2 (November 16, 4:30pm6:15pm)  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