2025 (Current Year) Faculty Courses School of Science Undergraduate major in Mathematics
Advanced Linear Algebra I
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Yuri Yatagawa
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Fri
- Class
- -
- Course Code
- MTH.A211
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 1Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course covers the concepts and examples of vector spaces and linear maps in linear algebra. Exercise problems will be presented in the lectures to cement understanding. This course is followed by "Advanced Linear Algebra II".
Knowledge in concrete linear algebra using matrices being assumed, this course deals with abstract treatment of vector spaces and linear maps. This is important not only in its own right but also as practical exercises for students to acquire basic skills in learning other fields of advanced mathematics.
Course description and aims
To understand important notions such as vector space, linear map, representation matrix, characteristic polynomial, eigenspace, Jordan normal form, etc., and to become able to make use of them.
Keywords
vector space, linear map, representation matrix, characteristic polynomial, eigenspace, Jordan normal form
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course accompanied by discussion sessions
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Vector space | Details will be provided during class session |
| Class 2 | Linear map | Details will be provided during class session |
| Class 3 | Representation matrix, eigenvalue | Details will be provided during class session |
| Class 4 | Minimal polynomial and characteristic polynomial | Details will be provided during class session |
| Class 5 | Generalized eigenspace | Details will be provided during class session |
| Class 6 | Normal form of a nilpotent matrix | Details will be provided during class session |
| Class 7 | Jordan normal form | Details will be provided during class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Takeshi Saito, ”The World of Linear Algebra”, University of Tokyo Press
Reference books, course materials, etc.
None specified
Evaluation methods and criteria
To be evaluated based on the final exams and reports. Details will be announced in the course.
Related courses
- LAS.M102 ： Linear Algebra I / Recitation
- LAS.M106 ： Linear Algebra II
- MTH.A212 ： Advanced Linear Algebra II
Prerequisites
Students are expected to have passed Linear Algebra I / Recitation and Linear Algebra II.