| 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 | 021917 | ||
| Instructor(s) | |||||
| 柴田 和樹 [SHIBATA Kazuki] | |||||
| Facility affiliation | Graduate School of Engineering | Office | afjgxte/L1151 | Email address | |
| Course description |
|
Linear algebra is the base on various field. In this course, we will learn basic properties of vector spaces and we will also learn about eigenvalues and eigenvectors, for deep understanding of linear algebra. Kazuki Shibata (a part-time lecturer) will be in charge of this course. |
| Expected Learning |
|
The goals of this course are (1) to compute bases and dimensions of vector spaces, (2) to be capable of performing their practical calculations. Corresponding criteria in the Diploma Policy: See the Curriculum maps |
| Course schedule |
|
1. Vector spaces and their subspaces 2. Linear independence and linear dependence 3. Maximum of linearly independent vectors 4. Bases and dimensions of vector spaces 5. Definition of linear maps and the kernel and the image of linear maps 6. Representation matrices of linear maps 7. Review, and midterm examination 8. Eigenvalues and eigenvectors 9. Diagonalization of square matrices 10. Inner product spaces: inner product of real vectors, orthogonal sets and orthogonal matrices 11. Orthonormal bases: Gram-Schmidt orthonormalization 12. Diagonalization of real symmetric matrices 13. Cayley-Hamilton theorem 14. Exercises 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 |
| References |
| Assessment/Grading |
| Midterm exam. (50%), Term exam. (50%) |
| Message from instructor(s) |
| Linear algebra Ⅱ is the abstract concept. For deep understanding, solve exercises. |
| Course keywords |
| Vector space, Basis, Dimension, Linear map, Representation matrix, Eigenvalues and eigenvectors, Diagonalization |
| Office hours |
| It will be announced in the first lecture. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 12/24/2019 3:27:16 PM |