Linear Algebra I Fall 2024
In this lecture we introduce the basic concepts about vector spaces, linear maps and matrix transformations. It is a very important basic course because In many occasions one approaches a problem by linearization, because linear systems are easier to solve than non-linear ones. The syllabus can be found here.
Content: (Organized by chapters in the lecture notes)
- Linear systems
- determinants
- Euclidean vector spaces
- General vector spaces
- Eigenvalues and eigenvectors
- Inner product space
- Diagonalization and quadratic forms
- Linear transforamations
Literature:
Book Name: Elementary Linear Algebra (Application Version),
Howard Anton & Chris Rorres, ISBN 978-1-118-43441-3, Wiley, 2014, Edition 11
Course (MATH1112.04): Wednesday (教学中心204) 8:15am-9:55am and
Friday (教学中心204) 8:15am-9:55am
TAs (time of example class with 10 min break)
Class 1 Guan Jingrong (Wed 6pm-7:40pm, 教学中心204,
Class 2 Zhao Yinhao (Wed 7:50pm-9:30pm, 教学中心203,
Every student needs to choose one example class and to write the number of the example class on the homework solution.
Exams:
- Midterm: Nov. 20th 数学中心204 8:15am-9:55am. Please be there by 7:45am. (closed book exam, no electronic equipment, bring pen and student id)
- Quizzes: There will be quizzes during the course for checking skills.
- Final: Jan. 15th. Wednesday (Week 18) 教学中心303, 8:00am-10:00am. Be there by 7:30 am, bring student ID, closed book, no electronic devices allowed.
Here is the sample exam for the midterm: Mock.pdf
Lecture notes Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5
Diagonalization Spectral norm Chapter 6 Chapter 7 Chapter 8
transformation matrix motivation
Additional material: Proof Thm25 (there are some typos)
Applications for the determinant
Problem sheets Sheet 1 Sheet 2 Sheet 3 (Page 94 and 101 for Sheet 3)
Sheet 4 Sheet 5 Sheet 6 Sheet 7 Sheet 8 Sheet 9 Sheet 10 Sheet 11
Sheet12 Sheet 13 Sheet14 Sheet15
Reviewing problems for the final
The solutions have to be handed in on Wednesdays before the lecture. Late submissions do not count.
Office hours: The office hours before the final exam are
Friday (10th Jan) 11am-1pm
Monday (13th Jan) 5pm-8pm.
You can also write an email or leave a Wechat message to arrange an appointement. My offfice is S413 in the Building of Creativity and Arts.
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