Course title
V14207001
Linear Algebra 2

 TAMORI Hiroyoshi
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.
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.
Goals and objectives
  1. To be able to diagonalize square matrices
  2. To be able to diagonalize real symmetric matrices by orthogonal 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
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 200minutes
Class assignment
2. Eigenvalue, Eigenvector, Characteristic polynomial Review the previous class 200minutes
Class assignment
3. Diagonalization of square matrices (1) Review the previous class 200minutes
Class assignment
4. Diagonalization of square matrices (2) Review the previous class 200minutes
Class assignment
5. Triangularization of square matrices, Cayley-Hamilton theorem Review the previous class 200minutes
Class assignment
6. Inner product, Gram–Schmidt orthonormalization Review the previous class 200minutes
Class assignment
7. Diagonalization of real symmetric matrices by orthogonal matrices, Diagonalization of Hermitian matrices by unitary matrices Review the previous class 200minutes
Class assignment
8. Mid-term exam and comments on it Review the previous classes 200minutes
9. Vector space, Subspace Review the previous class 200minutes
Class assignment
10. Linear independence, Basis, Dimension Review the previous class 200minutes
Class assignment
11. Linear map, Image and Kernel, Isomorphism of vector spaces Review the previous class 200minutes
Class assignment
12. Dimension theorem, Classification of finite dimensional vector spaces by dimension Review the previous class 200minutes
Class assignment
13. Matrix representation, Change of bases Review the previous class 200minutes
Class assignment
14. Final exam and comments on it Review the previous classes 200minutes
Total. - - 2800minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Class assignment Mid-term exam Final exam Total.
1. 10% 30% 5% 45%
2. 4% 7% 4% 15%
3. 8% 0% 20% 28%
4. 2% 0% 10% 12%
Total. 24% 37% 39% -
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 of order 3, 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.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in 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
Linear Algebra 1
Office hours and How to contact professors for questions
  • Office Hours: Wednesday 12:30-13:20
  • You can ask questions before/after each lecture.
  • 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 an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
Active-learning course
More than one class is 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 Sep 09 08:19:49 JST 2023