線性代數
Linear Algebra
| 節 | 週二 |
|---|---|
5 13:20–14:10 | 線性代數 YK436（陽明） 3 節連堂 |
6 14:20–15:10 | |
7 15:30–16:20 |
* 根據陽明交大上課時間表所列
Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The following topics will be included in this course: System of linear equations Matrix and vector algebra Determinants Eigenvalues and eigenvectors Linear transform Orthogonality Vector spaces Linear time invariant systems
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Linear algebra is the study of linear systems of equations, vector spaces, and linear transformations. Comfortably applying vectors and matrices is a basic ability of many mathematical procedures used for solving problems in science and engineering. In this class we will concentrate on the mathematical methods of linear algebra. The student will become competent in solving linear equations, performing matrix algebra, calculating determinants, and finding eigenvalues and eigenvectors, applying linear transform, understanding the concept of vector spaces and linear time invariant systems.
Homework: 20% Midterm exam: 40% Final exam: 40%
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction; Basic concepts on matrices and vectors 2022/9/13 |
| 第 2 週 | System of linear equations and Gaussian elimination 2022/9/20 |
| 第 3 週 | The language of set theory; Span of a set of vectors; Linear dependence and independence 2022/9/27 |
| 第 4 週 | Matrix multiplication; Invertibility and elementary matrices; The inverse of a matrix 2022/10/4 |
| 第 5 週 | Linear transformations and matrices; Composition and invertibility of linear transformations 2022/10/11 |
| 第 6 週 | Determinants 2022/10/18 |
| 第 7 週 | Subspaces and their properties; Basis and Dimensions; Coordinate systems 2022/10/25 |
| 第 8 週 | Mid-term exam 2022/11/1 |
| 第 9 週 | Eigenvalue, eigenvector, and diagnonalization (I) 2022/11/8 |
| 第 10 週 | Eigenvalue, eigenvector, and diagnonalization (II) 2022/11/15 |
| 第 11 週 | The geometry of vectors dot product; Orthogonal vector and projections 2022/11/22 |
| 第 12 週 | Orthogonal vector and projections; orthogonal projection matrices; 2022/11/29 |
| 第 13 週 | Least squares approximation 2022/12/6 |
| 第 14 週 | Symmetric matrices 2022/12/13 |
| 第 15 週 | Vector spaces and their subspaces; Linear transformation 2022/12/20 |
| 第 16 週 | Vector spaces: Basis and dimensions; Linear operators 2022/12/27 |
| 第 17 週 | Final Exam 2023/1/3 |
| 第 18 週 | Final Review 2023/1/10 |
Elementary Linear Algebra - A Matrix Approach, 2nd ed L. E. Spence, A. J. Insel and S. H. Friedberg
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