線性代數
Linear Algebra
| 節 | 週三 | 週五 |
|---|---|---|
3 10:10–11:00 | 線性代數 EC016（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 線性代數 EC016（光復） |
* 根據陽明交大上課時間表所列
This course introduces the fundamental concepts and methods of linear algebra, with an emphasis on topics that provide mathematical foundations for computer science. The course covers systems of linear equations, matrix algebra, vector spaces, linear independence, basis and dimension, linear transformations, determinants, eigenvalues and eigenvectors, diagonalization, orthogonality, least-squares problems, symmetric matrices, and the Singular Value Decomposition (SVD). By the end of the course, students should be able to perform standard linear algebra computations, understand the underlying mathematical structures, relate different representations of linear problems, and apply linear algebra techniques to selected problems in computer science and data analysis.
High-school mathematics or equivalent. No prior knowledge of linear algebra is assumed.
無備註
The course will be taught primarily through lectures and worked examples. Geometric interpretations and selected applications in computer science and data analysis will be introduced where appropriate to support conceptual understanding. Course materials, announcements, suggested exercises, and supplementary materials will be provided through the university e-learning platform. Teaching-assistant information and related arrangements will be announced at the beginning of the semester.
Exam 1: 30% Exam 2: 30% Cumulative Final Examination: 40% There is no graded homework. Suggested exercises may be provided for self-study and examination preparation. These exercises will not be submitted or graded. The detailed scope of each examination will be announced before the examination. The final examination is cumulative, with greater emphasis on material covered after Exam 2. Academic misconduct will be handled according to university regulations.
教師未提供此項資料
| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction; systems of linear equations; Gaussian and Gauss-Jordan elimination; echelon forms and solution sets. 時數：[2026-09-09]王偉豪(2.00) |
| 第 1 週 | Course introduction; systems of linear equations; Gaussian and Gauss-Jordan elimination; echelon forms and solution sets. 時數：[2026-09-11]王偉豪(1.00) |
| 第 2 週 | Vectors, linear combinations, span, and matrix equations; homogeneous systems and linear independence. 時數：[2026-09-16]王偉豪(2.00) |
| 第 2 週 | Vectors, linear combinations, span, and matrix equations; homogeneous systems and linear independence. 時數：[2026-09-18]王偉豪(1.00) |
| 第 3 週 | Matrix operations, matrix multiplication, transpose, and algebraic properties. 時數：[2026-09-23]王偉豪(2.00) |
| 第 3 週 | Matrix operations, matrix multiplication, transpose, and algebraic properties. 時數：[2026-09-25]王偉豪(1.00) |
| 第 4 週 | Inverse matrices and invertibility; vector spaces and subspaces; basis, coordinate vectors, and dimension. 時數：[2026-09-30]王偉豪(2.00) |
| 第 4 週 | Inverse matrices and invertibility; vector spaces and subspaces; basis, coordinate vectors, and dimension. 時數：[2026-10-02]王偉豪(1.00) |
| 第 5 週 | Row space, column space, and null space; rank, nullity, and the rank-nullity theorem. 時數：[2026-10-07]王偉豪(2.00) |
| 第 5 週 | Row space, column space, and null space; rank, nullity, and the rank-nullity theorem. 時數：[2026-10-09]王偉豪(1.00) |
| 第 6 週 | Exam 1 (30%, 100 minutes); Introduction to determinants and determinant computation. 時數：[2026-10-14]王偉豪(2.00) |
| 第 6 週 | Exam 1 (30%, 100 minutes); Introduction to determinants and determinant computation. 時數：[2026-10-16]王偉豪(1.00) |
| 第 7 週 | Properties of determinants; determinants and invertibility; geometric interpretation of determinants; introduction to linear transformations. 時數：[2026-10-21]王偉豪(2.00) |
| 第 7 週 | Properties of determinants; determinants and invertibility; geometric interpretation of determinants; introduction to linear transformations. 時數：[2026-10-23]王偉豪(1.00) |
| 第 8 週 | Linear transformations; kernel and range; one-to-one and onto transformations; matrix representations and coordinate changes. 時數：[2026-10-28]王偉豪(2.00) |
| 第 8 週 | Linear transformations; kernel and range; one-to-one and onto transformations; matrix representations and coordinate changes. 時數：[2026-10-30]王偉豪(1.00) |
| 第 9 週 | Eigenvalues and eigenvectors; characteristic equations; eigenspaces and algebraic and geometric multiplicities. 時數：[2026-11-04]王偉豪(2.00) |
| 第 9 週 | Eigenvalues and eigenvectors; characteristic equations; eigenspaces and algebraic and geometric multiplicities. 時數：[2026-11-06]王偉豪(1.00) |
| 第 10 週 | Diagonalization and similarity; matrix powers and selected applications. 時數：[2026-11-11]王偉豪(2.00) |
| 第 10 週 | Diagonalization and similarity; matrix powers and selected applications. 時數：[2026-11-13]王偉豪(1.00) |
| 第 11 週 | Inner products, norms, angles, orthogonality, and vector similarity. 時數：[2026-11-18]王偉豪(2.00) |
| 第 11 週 | Inner products, norms, angles, orthogonality, and vector similarity. 時數：[2026-11-20]王偉豪(1.00) |
| 第 12 週 | Exam 2 (30%, 100 minutes); Orthogonal complements and orthogonal projections. 時數：[2026-11-25]王偉豪(2.00) |
| 第 12 週 | Exam 2 (30%, 100 minutes); Orthogonal complements and orthogonal projections. 時數：[2026-11-27]王偉豪(1.00) |
| 第 13 週 | Orthonormal bases; the Gram-Schmidt process; QR factorization. 時數：[2026-12-02]王偉豪(2.00) |
| 第 13 週 | Orthonormal bases; the Gram-Schmidt process; QR factorization. 時數：[2026-12-04]王偉豪(1.00) |
| 第 14 週 | Least-squares problems; normal equations and QR-based solutions; data fitting; symmetric and positive semidefinite matrices. 時數：[2026-12-09]王偉豪(2.00) |
| 第 14 週 | Least-squares problems; normal equations and QR-based solutions; data fitting; symmetric and positive semidefinite matrices. 時數：[2026-12-11]王偉豪(1.00) |
| 第 15 週 | The spectral theorem and orthogonal diagonalization; Singular Value Decomposition (SVD); low-rank approximation and selected applications. 時數：[2026-12-16]王偉豪(2.00) |
| 第 15 週 | The spectral theorem and orthogonal diagonalization; Singular Value Decomposition (SVD); low-rank approximation and selected applications. 時數：[2026-12-18]王偉豪(1.00) |
| 第 16 週 | Cumulative Final Examination (40%, 100 minutes). 時數：[2026-12-23]王偉豪(2.00) |
| 第 16 週 | Cumulative Final Examination (40%, 100 minutes). 時數：[2026-12-25]王偉豪(1.00) |
Steven J. Leon and Lisette de Pillis, Linear Algebra with Applications, 10th ed., Pearson, 2020. The lecture sequence may differ from the chapter order of the textbook.
- 地點
- To be announced.
- 時間
- By appointment.
- 聯絡方式
- To be announced.