| 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 | 021922 | ||
| 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 specifi cally, we will fi rst learn basic propertiesof vector spaces and their bases. Then, we will also introduce the defi nition of linear maps and observe the relation betweenlinear maps and matrices. In particular, the properties of a change of basis will be investigated. Finally, we will learn abouteigenvalues 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] slylag6 1-2. Linear independence and linear dependence (pp.85-88) 3-4. Vector spaces and their subspaces (pp.90-94) 5. Bases and dimensions of vector spaces, the linear span of a set of vectors (pp.97-103) 6. Linear maps (pp.104-106) 7-8. Representation matrices of linear maps (pp.107-112) 9. Inner products, orthogonal systems and orthogonal matrices, complex inner products (pp.123-126, pp.134, except for Gram-Schmidt orthonormalization) 10. Gram-Schmidt orthonormalization, orthogonal matrix (pp.126-129, pp.132-133) 11. Eigenvalues and eigenvectors (pp.139-142) 12-13. Diagonalization of square matrices I (pp.106-110) 14. Diagonalization of real symmetric matrices (pp.155-158) 15. 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 specifi ed by the University and using the lecture handouts as well as the referencesspecifi ed below. |
| Required Text(s) and Materials |
| The same textbook as in Linear Algebra I will be used. |
| References |
| Miyake Toshitsune, “Nyuumon-Senkei-Daisuu”, Baifu-kan (in Jananese) |
| 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 diffi cult to understand at fi rst. However, in fact, they are closelylinked with the topics which we learned in Linear Algebra I. Concrete examples in the lecture or in the textbook will help toimprove your comprehension. |
| Course keywords |
| Vector space, Linear map, Basis, Dimension, Eigenvalue, Eigenvector, Diagonalization, Orthogonal matrix |
| Office hours |
| It will be announced in the fi rst lecture. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 9/20/2022 1:24:13 PM |