We will learn ...
This course will help you to understand the meaning and the properties of the determinant, which is critical for matrix diagonalization. We will then see many applications of matrix diagonalization: finding a nice coordinate system for a quadratic curve, solving a system of linear differential equations, solving a recurrence relation, and finding the matrix exponential. Theories behind the scene will be provided. Then we will move on to the theory of symmetric matrices, seeing they are always diagonalizable with an orthonormal eigenbasis and real eigenvalues. If time allows, we will go through various advanced topics, such as the principal component analysis, the interlacing theorem, the spectral clustering, and so on.
Determinant
a function that calculates the volumn of a matrix, which can be used to test invertibility
Diagonalization
finding the essence of a matrix: eigenvalues, eigenvectors
Theory of symmetric matrices
tons of applications of matrix diagonalization, including singular value decomposition, principal component analysis, spectral clustering ...
You need to do ...
HW0: Tell me your email before February 23 to get extra 2pt — this is a required work. Important information will be announced through email.
Participation (15%): There will be at least 15 in-class activities. Let's think, practice, and learn together in class.
Active Learning (10%): Learn actively and regularly. Reflect on what you have learned. Post a photo on Padlet, write a few sentences about what you have learned, and leave your student IDs. Names are optional. Each post before the final exam counts as 0.25 point.
Determinant
Quiz 1 (5%):
SampleQuiz1 [ pdf solution ]
Midterm 1 (20%):
Midterm1-A [ pdf solution ]
Midterm1-B [ pdf solution ]
Diagonalization
Quiz 2 (5%):
SampleQuiz2 [ pdf solution ]
Midterm 2 (20%):
Midterm2-A [ pdf solution ]
Midterm2-B [ pdf solution ]
Theory of symmetric matrices
Quiz 3 (5%):
SampleQuiz3 [ pdf solution ]
Final exam (20%):
Final-A [ pdf solution ]
Final-B [ pdf solution ]
Use the corresponding SampleQuiz to practice for each quiz.
No partial credits for quizzes. However, within the two weeks (and before each exam) after a quiz is given, you may ask for extra tests of the same question type. Your score for a quiz is the average of all tests you have taken under the same question type. Note: If you missed the quiz in class, that counts as a zero.
For example, you missed Quiz 1 in class, and you asked for 3 extra tests and get 2 of them correct, then your score for Quiz 1 is (0 + 5 + 5 + 0) / 4 = 2.5.
Use learning resources to practice for each eaxm.
Course Info
- Term: Feb 19, 2024 – Jun 21, 2024
- Meeting time: Monday, 9:10 am – 11:00 am @ SC0014
- Meeting time: Wednesday, 9:10 am – 10:00 am @ SC0014
- Recitation: Monday, 2:10 pm – 3:00 am @ SC1003
- Instructor: Jephian Lin | 林晉宏
- Email: chlin [at] math.nsysu.edu.tw
- Office: SC2002-5
- Office Hours: Tuesday, 4:10 pm – 5:00 pm
- Office Hours: Thursday, 4:10 pm – 5:00 pm
- TA: Anzila Laikhuram
- Email: angi286 [at] gmail.com
- Office: SC2008
- Office Hours: By appointment
- Discord: https://discord.com/invite/behbC9NmqNJ
Textbook
Linear algebra notebook
Jephian Lin
Linear Algebra [ pdf answers ]
Jim HefferonCourse website
Further Resources
Essence of linear algebra
3Blue1Brown
LA Tea: 利用喝杯茶的時間，來聊點線性代數吧！
Linear Algebra Done Right
Sheldon Axler
Tentative Schedule
Policies/Ethics
Accessibility
Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me.
Grading
Percentage scores will be converted to letter grades according to the university-wide standard table.
Attendance
You are expected to attend the classes.
Missing work
If you miss some course components due to illness, accident, family affliction, or religious observances, please talk to me and provide the documentation. In such cases, the course component is excused, and your course score will be calculated by distributing the weight of the missed item(s) across the other course components. Missing components are limited to at most 20%.
Academic integrity
Do not copy others' work, including others' homework, the textbook, online materials, and others' answers in an exam; if it is really necessary, add proper citations to your references. It makes no point (and gives you no point) if the work is not yours since you learned nothing.