### 2022　Advanced Linear Algebra I

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Instructor(s)
Taguchi Yuichiro
Class Format
Lecture    (Livestream)
Media-enhanced courses
Day/Period(Room No.)
Fri3-4(H112)
Group
-
Course number
MTH.A211
Credits
1
2022
Offered quarter
1Q
Syllabus updated
2022/3/16
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

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.

### Student learning outcomes

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 that will be developed

 ✔ 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/Required learning

Course schedule Required learning
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

### Out-of-Class Study Time (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.

None specified

### Reference books, course materials, etc.

Takeshi Saito, ”The World of Linear Algebra”, University of Tokyo Press

### Assessment criteria and methods

To be evaluated based on exercises in discussion sessions and the final exam as a whole. Details will be announced during the course.

### Related courses

• LAS.M102 ： Linear Algebra I / Recitation
• LAS.M106 ： Linear Algebra II
• MTH.A212 ： Advanced Linear Algebra II

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed Linear Algebra I / Recitation and Linear Algebra II.