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
Linear functions
functions that preserve structure and its matrix representation
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 21 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%): Do some exercises in the textbook and think about what you have learned. Use Padlet to record your learning activities. Each post before the final exam counts as 1 point.
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.
A few tips for learning mathematics ...
Mistakes Make You Smarter: Everyone learns through experiences and mistakes. For each new concept you learn, generate as many examples as possible to train your brain to distinguish between right and wrong.
Ask Questions: Beyond knowledge, mathematics is fundamentally about logic. Question everything you encounter—why it is defined this way, why an assumption is required, why a proof needs a particular step, and so on.
Think Carefully: Sound arguments should hold true in any circumstance. Verify the examples you generate to ensure they align with your argument.
Help Each Other: Learning together can make the process easier. Teaching others is also an effective way to reinforce your own understanding.
Course Info
- Term: Feb 17, 2025 – Jun 20, 2025
- Meeting time: Wednesday, 2:10 pm – 4:00 pm @ SC0008
- Meeting time: Thursday, 11:10 am – 12:00 noon @ SC0008
- Recitation: Thursday, 12:10 noon – 1:00 pm @ SC0008
- Instructor: Jephian Lin | 林晉宏
- Email: chlin [at] math.nsysu.edu.tw
- Office: SC2002-5
- Office Hours: Tuesday, 3:10 pm – 5:00 pm
- Office Hours: Thursday, 3:10 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
Jim HefferonCourse website
Further Resources
Linear algebra notebook
Jephian Lin
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.