Course title
3100330V1
Linear Algebra 2

 TAMORI Hiroyoshi
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Mathematical Sciences Course DP-1・3・1 自然科学、情報技術に関する基礎的知識を理解し、利用できる。
Purpose of class
We become able to calculate eigenvalues, eigenvectors, and diagonalization of square matrices. We learn fundamental concepts of the theory of vector space, and associate them with explicit calculation of matrices.
Course description
This is a continuation of ”Linear Algebra 1”. In the first half of the course, we learn eigenvalues, eigenvectors, diagonalization of square matrices, and their application. In the latter half, we learn basics of the theory of vector spaces.
Goals and objectives
  1. To be able to diagonalize square matrices
  2. To be able to diagonalize Hermitian matrices by unitary matrices
  3. To be able to explain the definitions of vector space, subspace, linear map, image and kernel, basis, and dimension
  4. To understand the notion of matrix representation, and to be able to explain its concrete examples
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Class assignment Mid-term exam Final exam Total.
1. 5% 20% 5% 30%
2. 5% 20% 10% 35%
3. 5% 0% 15% 20%
4. 5% 0% 10% 15%
Total. 20% 40% 40% -
Evaluation method and criteria
Students are evaluated by Class assignments (about 20%), Mid-term exam (about 40%), and Final exam (about 40％). One criterion for earning credits is to be able to check diagonalizability of a given square matrix, to be able to diagonalize it if it is diagonalizable, and to be able to explain the definitions and examples of basic notions in the theory of vector spaces.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Guidance, What is Diagonalization? Review of Linear Algebra 1 100minutes
Class assignment 100minutes
2. Eigenvalue, Eigenvector, Characteristic polynomial Review the previous class 100minutes
Class assignment 100minutes
3. Diagonalization of square matrices (1) Review the previous class 100minutes
Class assignment 100minutes
4. Diagonalization of square matrices (2) Review the previous class 100minutes
Class assignment 100minutes
5. Triangularization of square matrices, Cayley-Hamilton theorem Review the previous class 100minutes
Class assignment 100minutes
6. Inner product, Gram–Schmidt orthonormalization Review the previous class 100minutes
Class assignment 100minutes
7. Diagonalization of real symmetric matrices by orthogonal matrices, Diagonalization of Hermitian matrices by unitary matrices Review the previous class 100minutes
Class assignment 100minutes
8. Mid-term exam Review the previous classes 200minutes
9. Vector space, Subspace Review the previous class 100minutes
Class assignment 100minutes
10. Linear independence, Basis, Dimension Review the previous class 100minutes
Class assignment 100minutes
11. Linear map, Image and Kernel Review the previous class 100minutes
Class assignment 100minutes
12. Isomorphism of vector spaces, Dimension theorem, Classification of finite dimensional vector spaces by dimension Review the previous class 100minutes
Class assignment 100minutes
13. Matrix representation Review the previous class 100minutes
Class assignment 100minutes
14. Final exam Review the previous classes 200minutes
Total. - - 2800minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in/outside the class.
Textbooks and reference materials
【Reference book】
Tatsuo SUZUKI and Katsunori ANO ”講義：線形代数 （第2版）”（Gakujutsu Tosho Shuppan-sha co.,Ltd., ISBN 978-4-7806-0477-1）
Toshitsune MIYAKE, ”入門線形代数” (Baihu-kan co.,Ltd., ISBN 978-4563002169)
Koji HASEGAWA ”線型代数［改訂版］” (Nippon Hyoron sha co.,Ltd., ISBN 978-4-535-78771-1)

Students do not need to purchase the above books. These can be used for self-study and exercises.
Prerequisites
Office hours and How to contact professors for questions
  • You can ask questions before/during/after each lecture.
  • Office Hours: Wednesday 12:30-13:20
  • You can ask questions at the educational support section.
  • You can visit the office of the lecturer and ask questions.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates a basic self-management skills
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Sat Mar 14 14:39:08 JST 2026