| Course title | |||||
| 線形代数学Ⅱ [Linear Algebra Ⅱ] | |||||
| Course category | technology speciality courses | Requirement | Credit | 2 | |
| Department | Department of Biomedical Engineering, Applied Physics(~2018) | 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. Takashi Yoguchi (a part-time lecturer) will be in charge of this course. |
| 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) performing diagonalization of square matrices. Corresponding criteria in the Diploma Policy: See the Curriculum maps. |
| Course schedule |
|
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. Exercises I 6. Linear maps (p.87, p.91) 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. Diagonalization of real symmetric matrices (pp.121-126) 14. Exercises II 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. Toshitune Miyake, “Nyuumon Senkei Daisuu” (in Japanese) |
| References |
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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 |
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The term examination will constitute 80% of your grade and two exercises (the 7th and 14th weeks) constitute 20% of your grade. (Grade distribution of last year: S 4% A 31% B 29% C 29% D 7%) |
| 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 |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Language Subject |
| Last update |
| 6/3/2019 12:58:50 PM |