| Course title | |||||
| 線形代数学Ⅱ [Linear Algebra Ⅱ] | |||||
| Course category | technology speciality courses | Requirement | Credit | 2 | |
| Department | Year | 1～4 | Semester | 3rd | |
| Course type | 3rd | Course code | 021918 | ||
| Instructor(s) | |||||
| 與口 卓志 [YOGUCHI Takashi] | |||||
| Facility affiliation | Graduate School of Agriculture | Office | Email address | ||
| Course description |
| In this course, the notion of vector spaces and linear maps are introduced. More specifically, we will first learn basic properties of vector spaces and their bases. Then, we will also introduce the definition of linear maps and observe the relation between linear maps and matrices. In particular, the properties of a change of basis will be investigated. Finally, we will learn about eigenvalues and eigenvectors of matrices and their applications. |
| Expected Learning |
|
The goal of this course is to be capable of: (1) constructing a basis of a given vector space, (2) calculating eigenvalues and eigenvectors of square matrices of order 3, (3) solving problems about inner product of vectors and orthonormal bases, (4) performing diagonalization of square matrices. Corresponding criteria in the Diploma Policy: See the Curriculum maps. |
| Course schedule |
|
Google Classroom will be used for quizzes and assignments in each week. [Google Classroom Code] 4aieudk 1. Vector spaces and their subspaces (pp.63-66) 2. Linear independence and linear dependence (pp.68-73) 3. On the maximum number of linearly independent vectors in a vector space (pp.75-79) 4. Bases and dimensions of vector spaces, the linear span of a set of vectors (pp.81-85) 5. Linear maps (p.87, p.91) 6-7. Representation matrices of linear maps (pp.92-96) 8. Eigenvalues and eigenvectors (pp.98-104) 9-10. Diagonalization of square matrices I (pp.106-110) 11. Inner products, orthogonal systems and orthogonal matrices (pp.112-121 except for Gram-Schmidt orthonormalization) 12. Gram-Schmidt orthonormalization, complex inner products (pp.116-117, p.121) 13-14. Diagonalization of real symmetric matrices (pp.121-126) 15. Review, and Term examination |
| Prerequisites |
|
Knowledge of the course of Linear Algebra I will be used in the lecture. In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University and using the lecture handouts as well as the references specified below. |
| Required Text(s) and Materials |
|
The same textbook as in Linear Algebra I is used. |
| References |
|
Masayasu Murakami et al., “Enshuu Senkei-Daisuu”, Baifu-kan (in Japanese), Noburou Ishii et al., “Rikou-kei Sin-Katei Senkei-Daisuu”, Baifu-kan (in Japanese) |
| Assessment/Grading |
|
The term examination, 70%; Quizzes in Google Classroom, 10%; Assignments, 20% |
| Message from instructor(s) |
| Some topics introduced in this course may seem abstract and difficult to understand at first. However, in fact, they are closely linked with the topics which we learned in Linear Algebra I. Concrete examples in the lecture or in the textbook will help to improve your comprehension. |
| Course keywords |
| Vector space, Linear map, Basis, Dimension, Eigenvalue, Eigenvector, Diagonalization, Orthogonal matrix |
| Office hours |
| It will be announced in the first lecture. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 9/20/2022 1:16:10 PM |