Course title
3100330Q1
Linear Algebra 2

 KAJIGAYA Toru
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Mechatronics 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
Students will understand the concepts of linear independence of vectors and basis, and be able to determine them through computation. In addition, they will learn matrix diagonalization, including diagonalization of real symmetric matrices by orthogonal matrices.
Course description
Following Linear Algebra I, this course continues the study of matrix theory. In the first half, we review Gaussian elimination and the computation of determinants, and then study linear independence of vectors and the concept of basis. In the second half, we cover the general theory of matrix diagonalization, including the diagonalization of real symmetric matrices by orthogonal matrices, along with their applications.
Goals and objectives
  1. To be able to compute Gaussian elimination and determinants
  2. To be able to understand the concepts of linear independence and basis, and be able to determine them through computation.
  3. To be able to diagonalize matrices
  4. To be able to diagonalize real symmetric matrices by orthogonal matrix
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term examination Term-end examination Total.
1. 20% 5% 25%
2. 20% 5% 25%
3. 0% 30% 30%
4. 20% 20%
Total. 40% 60% -
Evaluation method and criteria
The mid-term exam will be evaluated as 40%, the final exam as 60%. Students will pass the class when they are judged to have understood at least 60% of the content covered in the class (total score: 60 points or more).
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Review of Linear algebra 1 Review of Linear Algebra 1 200minutes
2. Computation of determinants by Gaussian elimination Review 200minutes
3. Cofactor expansion Review 200minutes
4. Linear independence of vectors Review 200minutes
5. Determination of linear independence Review 200minutes
6. Basis of vector spaces Review 200minutes
7. Mid-term examination and comments on it Review all 200minutes
8. Eigenvalues and eigenvector Review 200minutes
9. Diagonalization of square matrices (1) Review 200minutes
10. Diagonalization of square matrices (2) Review 200minutes
11. Orthonormal basis Review 200minutes
12. Diagonalization of real symmetric matrices Review 200minutes
13. Applications of diagonalization Review 200minutes
14. Term-end examination and comments on it Review all 200minutes
Total. - - 2800minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
教科書：三宅敏恒著、入門線形代数、培風館
参考書：長谷川浩司著、線型代数、日本評論社. 高松瑞代著、応用がみえる線形代数、岩波書店.
Prerequisites
Students are expected to review Linear Algebra 1.
Office hours and How to contact professors for questions
  • Basically, inquiries will be handled before or after class, during office hours, or by email.
    Office hours: Monday 17:00–18:00.
    The email address will be provided at the beginning of the course.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
  • Course that cultivates an ability for utilizing knowledge
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
Last modified : Sat Apr 04 04:02:26 JST 2026