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| Linear Algebra U | |
| 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. |
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| 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 |
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| Course schedule | |
| 1. Vector spaces 2. Vector spaces and their subspaces 3. Linear independence and linear dependence 4. Maximum of linearly independent vectors 5. Bases and dimensions of vector spaces 6. Linear maps 7. Representation matrices of linear maps 8. Review, and midterm examination 9. Eigenvalues and eigenvectors 10. Diagonalization of square matrices 11. Inner products and complex numbers 12. Orthonormalization and orthogonal matrices 13. Diagonalization of real symmetric matrices 14. Cayley-Hamilton theorem 15. Review, and Term examination |
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| 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. |
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| Required Text(s) and Materials | |
| Textbooks will be introduced in the first lecture, if necessary. |
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| References | |
| Miyake Toshitsune, gNyuumon-Senkei-Daisuuh, Baifu-kan (in Jananese) |
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| Assessment/Grading | |
| 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 |
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| Office hours | |
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