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.
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.
vector space, linear map, representation matrix, characteristic polynomial, eigenspace, Jordan normal form
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
Standard lecture course accompanied by discussion sessions
|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|
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.
Takeshi Saito, ”The World of Linear Algebra”, University of Tokyo Press
To be evaluated based on exercises in discussion sessions and the final exam as a whole. Details will be announced during the course.
Students are expected to have passed Linear Algebra I / Recitation and Linear Algebra II.