MATH2040A - Linear Algebra II - 2024/25

Announcement

• Aug 29: Welcome to the course. No tutorial in the first week. Here is the course outline [PDF]: [Download file]

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General Information

Lecturer

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

Teaching Assistant

• Mr. Kam Fai CHAN
  • Office: LSB 232
  • Tel: 3943 5294
  • Email:
• Mr. Junhao ZHANG
  • Office: LSB 232
  • Tel: 3943 5294
  • Email:

Time and Venue

• Lecture: Monday 15:30-16:15 Mong Man Wai Bldg 710; Thursday 16:30-18:15 Mong Man Wai Bldg 710
• Tutorial: Monday 16:30-17:15 Mong Man Wai Bldg 710; Thursday 15:30-16:15 Mong Man Wai Bldg 710

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.
• Strang, Linear Algebra and Its Applications, 4th edition, Cengage Learning.

Pre-class Notes

• Full Review Note

Lecture Notes

• LN01: Vector Space
• LN02: Subspace
• LN03: Span, Linearly (in-)dependent
• LN04: Basis, (In-)finite-dimensional, Dimension
• LN05: Linear Transformations
• LN06: Null space, Range, Dimension Theorem
• LN07: Matrix Representation of a Linear Transformation
• LN08: Invertibility, Isomorphism
• LN09: Change of Coordinates
• LN10: Eigenvalue, Eigenvector, Diagonalizable Linear Transformation
• LN11: Diagonalizability
• LN12: Invariant Subspace, Cayley-Hamilton Theorem
• LN13: Inner Product Space
• LN14: Gram-Schmidt Orthogonalization
• LN15: Orthogonal Complement
• LN16: Adjoint of a Linear Operator
• LN17: Characterisation of Normal and Self-Adjoint Operators
• LN18: Unitary/Orthogonal Operators
• LN19: Spectral Decomposition

Tutorial Notes

• Tutorial 1
• Tutorial 2
• Tutorial 3
• Tutorial 4
• Tutorial 5
• Tutorial 6
• Tutorial 7
• Tutorial 8
• Tutorial 9
• Tutorial 10
• Tutorial 11
• Tutorial 12

Assignments

• Homework 01
• Homework 02
• Homework 03
• Homework 04
• Homework 05
• Homework 06
• Homework 07
• Homework 08
• Homework 09
• Homework 10
• Homework 11 (no need to hand in)

Solutions

• Suggested solutions to Homework 1
• Suggested solutions to Homework 2
• Suggested solutions to Homework 3
• Suggested solutions to Homework 4
• Suggested solutions to Homework 5
• Suggested solutions to Homework 6
• Suggested solutions to Homework 7
• Suggested solutions to Homework 8
• Suggested solutions to Homework 9
• Suggested solutions to Homework 10
• Suggested solutions to Homework 11

Assessment Scheme

Homework (about ten times)		10%
Midterm Test (Time and date: 1830-2030 Oct 25 Friday; Venue: SWH 1 (G/F) at Fung King Hey Building (KHB))		40%
Final (TBA by University)		50%

Useful Links

• Axler, Linear Algebra Done Right, 3rd edition, Springer.
• Strang, Linear Algebra and Its Applications, 4th edition, Cengage Learning.
• Textbook via CUHK library

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, 2024 00:32:42