MATH2040A - Linear Algebra II - 2022/23

Announcement

• Aug 29: Welcome to the course. Here is the course outline [PDF]: [Download file]
• Sep 5: In the 1st week Tutorial Lecture on Sep 8th Thursday has changed to Course Lecture. Thus, the course lecture on Sep 8th will start from 4:30pm and end at 6:15pm.
• Sep 23: Be reminded that Test 1 will start at 1830 on October 12 Wed with duration 90 minutes (Venue: LSB LT6). It is a close-book test covering 6 topics from Topic 1 to Topic 6 (see the course review notes below).
• Nov 4: Be reminded that Test 2 will start at 1830 on November 16th Wed with duration 90 minutes (Venue: LSB LT6). It is a close-book test covering 6 topics from Topic 7 to Topic 12 (see the course review notes below).

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General Information

Lecturer

• Prof Renjun DUAN
  • Office: LSB 206
  • Tel: 3943 7977
  • Email:

Teaching Assistant

• Mr. Zongguang LI
  • Office: LSB 232
  • Tel: 3943 5294
  • Email:
• Mr. Kam Fai CHAN
  • Office: LSB 232
  • Tel: 3943 5294
  • Email:

Time and Venue

• Lecture: Tuesday 10:30-12:15 Yasumoto Int'l Acad Park LT2; Thursday 16:30-17:15 Lady Shaw Bldg LT3
• Tutorial: Thursday 17:30-18:15 Lady Shaw Bldg LT3

Course Description

This course is a continuation of Linear Algebra I (MATH 1030). It is a second course on linear algebra and will cover basic concepts of abstract vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalizability, operators on inner product spaces, orthogonality and Gram-Schmidt process, adjoint, normal and self-adjoint operators, spectral theorems, and if time permits, quadratic forms 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.

References

• Axler, Linear Algebra Done Right, 3rd edition, Springer.

Pre-class Notes

• Full Review Note
• Jordan form

Lecture Notes

• Topic01 (Vector space)
• Topic02 (Subspace)
• Topic03 (Span, Linearly independent)
• Topic04 (Basis, Dimension)
• Topic05 (Linear transformation)
• Topic06 (Dimension theorem)
• Topic07 (Matrix representation)
• Topic08 (Invertibility)
• Topic09 (Change of coordinates matrix)
• Topic10 (Eigenvector)
• Topic11 (Diagonalizability)
• Topic12 (Cayley-Hamilton Theorem)
• Topic13 (Inner product space)
• Topic14 (Gram-Schmidt orthogonalization)
• Topic15 (Orthogonal complement)
• Topic16 (Adjoint of a linear operator)
• Topic17 (Normal/Self-adjoint operator)
• Topic18 (Unitary/Orthogonal operator)
• Topic19 (Spectral decomposition)

Assignments

• HW01
• HW02
• HW03
• HW04
• HW05
• HW06
• HW07
• HW08
• HW09
• HW10 (extended to Dec 6th Tuesday)

Quizzes and Exams

• Test 1
• Suggested sol to Test 1
• Test 2
• Suggested sol to Test 2

Solutions

• HW1 Sol
• HW2 Sol
• HW3 Sol
• HW4 Sol
• HW5 Sol
• HW6 Sol
• HW7 Sol
• HW8 Sol
• HW9 Sol
• HW10 Sol

Assessment Scheme

Homework (about ten times)		10%
Test 1 (Time and date: 1830-2000 Oct 12 Wed; Venue: LSB LT6)		20%
Test 2 (Time and date: 1830-2000 Nov 16 Wed; Venue: LSB LT6)		20%
Final (TBA by university)		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.

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Assessment Policy

Last updated: November 29, 2022 14:50:44