| Course title | |||||
| 線形代数学Ⅱ [Linear Algebra Ⅱ] | |||||
| Course category | Requirement | Credit | 2 | ||
| Department | Year | 2～ | Semester | 3rd | |
| Course type | 3rd | Course code | 01ma2003 | ||
| Instructor(s) | |||||
| 金城 謙作 [KINJO Kensaku] | |||||
| Facility affiliation | Graduate School of Agriculture | Office | Email address | ||
| Course description |
|
Linear algebra provides indispensable tools to analyze various mathematical phenomena appearing in engineering. In this course, the notion of a vector space and a linear map between two vector spaces will be introduced. We will learn various basic properties of a basis and the dimension of a vector space, and the image and the kernel of a linear map. We will also learn about an eigenvalue and an eigenvector, for deep understanding of linear algebra. This course is taught by a part-time lecturer. Once the employment of the part-time lecturer is confirmed, this syllabus may be modified. In this case, the official version is the modified syllabus. |
| Expected Learning |
|
The goals of this course are (1) to understand vector spaces, linear maps, eigenvalues, eigenvectors, inner products and diagonalization, and (2) to be capable of performing their practical calculations. Corresponding criteria in the Diploma Policy: See the Curriculum maps. (URL: https://www.tuat.ac.jp/campuslife_career/campuslife/policy/ ) |
| Course schedule |
|
1. Vector spaces 2. Vector spaces and their subspaces 3. Linear independence and linear dependence 4. Bases and dimensions of vector spaces 5. Linear maps 6. Image and Kernel of linear maps 7. Representation matrices of linear maps 8. Eigenvalues and eigenvectors 9. Diagonalization of square matrices 10. Applications of diagonalization of square matrices 11. Inner products of vectors 12. Gram-Schmidt orthonormalization of vectors 13. Orthonormalization and orthogonal matrices 14. Diagonalization of real symmetric matrices 15. Exercise 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 |
| References |
| Miyake Toshitsune, “Nyuumon-Senkei- Daisuu”, Baifu-kan (in Jananese) |
| Assessment/Grading |
| Term examination (100%) |
| Message from instructor(s) |
| Course keywords |
| Vector space, Linear map, Linear independence and linear dependence, Basis, Dimension, Eigenvalues and eigenvectors, Diagonalization of real symmetric matrix |
| Office hours |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 9/22/2022 4:04:20 PM |