2025 (Current Year) Faculty Courses Liberal arts and basic science courses Basic science and technology courses
Linear Algebra Recitation II T(71～80)
- Academic unit or major
- Basic science and technology courses
- Instructor(s)
- Shingo Kawai
- Class Format
- Exercise
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- T(71～80)
- Course Code
- LAS.M108
- Number of credits
- 010
- Course offered
- 2025
- Offered quarter
- 4Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Based on "Linear Algebra I/Recitation", this course covers basic part of vector space and linear mapping, eigenvalue and diagonalization, and inner product of vector space.
The aim of this recitation is to cultivate a better understanding of the theory of vector spaces which will be important for
science and engineering.
Course description and aims
Following "Linear algebra I/Recitation", this course is concerned with the foundation of linear algebra. This course aims for a deeper understanding and development of the theory of Linear Algebra.
Keywords
Vector space, basis, linear transformation, eigenvalue, diagonalization
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
A recitation class is held every week.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Vector space, subspace | Help better understand the notions of vector space. |
| Class 2 | Linear combination, linear independence, linear dependence | Help better understand the notion of linear independence. |
| Class 3 | Basis, dimension, existence of basis | Help better understand the notion of basis. |
| Class 4 | Linear transformation, kernel and image, representation matrix of linear transformation | Help better understand linear transformation and related notions. |
| Class 5 | Orthonormal basis, inner product and norm, Schwarz's inequality, orthogonalization method of Schmitt | Help better understand orthonormal basis and related notion. |
| Class 6 | Eigenvalue, eigenvector, characteristic polynomial, multiplicity, eigenspace, triangularization and diagonalization of matrices | Help better understand eigenvalue problems. |
| Class 7 | Diagonalization of normal matrices, diagonalization of real symmetric matrix | Help better understand diagonalization and related notions. |
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)
See the syllabus of Linear Algebra II, Class T (LAS.M106-09).
Reference books, course materials, etc.
See the syllabus of Linear Algebra II, Class T (LAS.M106-09).
Evaluation methods and criteria
Based on overall evaluations of the results of quizzes, reports, mid-term, and final examinations. Details will be announced in class.
Related courses
- LAS.M102 ： Linear Algebra I / Recitation
- LAS.M106 ： Linear Algebra II
Prerequisites
Students are supposed to have completed Linear Algebra I / Recitation (LAS.M102).
Students are recommended to take Linear Algebra II (LAS.M106) at the same time.
Other
None in particular.