2020 Faculty Courses School of Science Undergraduate major in Mathematics
Advanced Linear Algebra II
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Shin-Ichiro Mizumoto
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Wed (H135)
- Class
- -
- Course Code
- MTH.A212
- Number of credits
- 100
- Course offered
- 2020
- Offered quarter
- 2Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Students in this course will study the concept and examples of vector space in linear algebra. Exercise problems will be presented in class to cement understanding. This course follows "Advanced Linear Algebra I. "
Prior experience with linear algebra using specific matrices is assumed, and this course discusses in detail from the basics of vector space to linear mapping to eigenvalues and the like. These activities are important, also serving as practical exercises for students to acquire basic methods in learning other fields of advanced mathematics.
Course description and aims
Important notions are as follows:
vector space, linear span, linear map, isomorphism, commutative diagram, representation matrix, eigenvalue, eigenspace.
Keywords
linear map, dual space, quotient space
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 | Isomorphism and applications | Details will be provided during each class session |
| Class 2 | representation matrix | Details will be provided during each class session |
| Class 3 | change of basis and commutative diagram | Details will be provided during each class session |
| Class 4 | eigenvalue and eigenspace | Details will be provided during each class session |
| Class 5 | invariant subspace | Details will be provided during each class session |
| Class 6 | application of diagonalization | Details will be provided during each class session |
| Class 7 | quotient space, dual space | Details will be provided during each 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)
None required
Reference books, course materials, etc.
Saito, Masahiko Introduction to Linear Algebra, University of Tokyo Press
Evaluation methods and criteria
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
- MTH.A211 ： Advanced Linear Algebra I
Prerequisites
Students are expected to have passed Advanced Linear Algebra I