| 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 | 021920 | ||
| Instructor(s) | |||||
| 木原 裕充 [] | |||||
| Facility affiliation | Graduate School of Engineering | Office | Email address | ||
| Course description |
|
In this course we introduce the notion of an abstract vector space as a generalization of the space of plane or space vectors, as well as a linear map between two vector spaces, which is studied with its matrix representation. In particular, we will learn about basic properties and computation of a basis and the dimension of a vector space, the image and kernel of a linear map. We also learn about the concepts and methods of eigen values and eigen spaces, diagonalization, and metric spaces, aiming at better 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. class code: qsrjqq4 |
| Expected Learning |
|
The goal of this course is: 1) to understand basic notions of vector spaces, linear maps, linear independence and bases 2) capable to calculate (bases of) the image and kernel of a linear map given by a matrix 3) capable to calculate the representation matrix of a linear map with respect to given bases 4) capable to calculate the eigen values and eigen spaces of a square matrix and determine whether it is diagonalizable 5) capable to ortho-normalize a given basis of a metric space Corresponding criteria in the Diploma Policy: See the Curriculum maps |
| Course schedule |
|
1. Numerical vectors and systems of equations 2. Vector spaces and their subspaces 3. Linear independence and linear dependence 4. Maximum number of linearly independent vectors 5. Bases and dimensions of vector spaces 6. Linear maps 7. Representation matrices of linear maps 8. isomorphism, eigenvalues and eigenvectors 9. Diagonalization of square matrices 10. inner products and Hermitian inner product 11. Schmidt's orthogonalization method and orthogonal matrices 12. Diagonalization of real symmetric matrices 13. Generalized eigenspaces 14. Normal matrices, Jordan normal forms 15. Term examination * This schedule may be changed to be suit interest and understanding of students |
| Prerequisites |
|
Contents of "Linear Algebra I" in the spring semester. 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 |
| Miyake, T.: "Nyuumon-Senkei-Daisuu", Baifu-kan (in japanese) |
| References |
| To be indicated in the lecture |
| Assessment/Grading |
| Midterm examination (50%) + Term examination (50%) |
| Message from instructor(s) |
| Course keywords |
| vector space, linear map, linear independence, basis, dimension, representation matrix, eigenvalue, eigenspace, diagonalization, inner product |
| Office hours |
| t will be announced in the first lecture. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 10/5/2022 9:24:38 PM |