線性代數
Linear Algebra
| 節 | 週三 | 週五 |
|---|---|---|
3 10:10–11:00 | 線性代數 EC114（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 線性代數 EC114（光復） |
* 根據陽明交大上課時間表所列
Goals of the Course: This introductory course in Linear Algebra focuses on concepts and techniques relevant to the modern field of linear algebra. By the end of the course, students should be able to explain the fundamental concepts of linear algebra and apply the theory to practical examples. Course Outline: 1. Solving linear equations of the form Ax = b using Gaussian and Gauss-Jordan elimination; understanding echelon forms. 2. Matrix algebra: operations, inverses, and the criteria for invertibility. 3. Subspaces of R^n: exploring column space, null space, linear independence, basis, dimension, and rank. 4. Determinants: definitions, properties, and applications. 5. Eigenvalues and eigenvectors: the characteristic equation, diagonalization, similarity, and change of basis. 6. Orthogonality: inner product, orthogonal projections, the Gram-Schmidt process, and least-squares problems. 7. Symmetric matrices, quadratic forms, and the Singular Value Decomposition (SVD). 8. Application highlights, such as motivating examples including PageRank, cosine similarity and embeddings, linear regression, Principal Component Analysis (PCA), and recommender systems.
High-school level mathematics. No university-level prerequisites. This is an EMI course: lectures, materials, and exams are entirely in English.
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Three in-class exams, 100% of the grade. * Exam 1: Week 6 (Wed 2026-10-14), covering weeks 1-5. * Exam 2: Week 12 (Wed 2026-11-25), covering weeks 6-10. * Exam 3: Week 16 (Wed 2026-12-23), covering weeks 12-15. * The detailed scope of each exam will be announced before the exam. * Homework: suggested problem sets from the textbook will be assigned regularly. Homework is not graded; it serves as practice and exam preparation. * 考試作弊，學期成績以零分計，並送校方處理。
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction Systems of linear equations Row reduction and echelon forms |
| 第 2 週 | Vector equations; matrix equations Solution sets of linear systems |
| 第 3 週 | Linear independence; introduction to linear transformations The matrix of a linear transformation 9/25 (Friday) Mid-Autumn Festival: no class |
| 第 4 週 | Matrix operations; inverse matrices Characterizations of invertible matrices |
| 第 5 週 | Subspaces of R^n; dimension and rank 10/9 (Friday) National Day holiday: no class |
| 第 6 週 | 10/14 (Wednesday) Exam #1 (weeks 1–5) Determinants: introduction |
| 第 7 週 | Properties of determinants Applications of determinants: Cramer's rule, area and volume |
| 第 8 週 | Eigenvalues and eigenvectors The characteristic equation |
| 第 9 週 | Diagonalization Similarity and change of basis Application spotlight, e.g., Markov chains → PageRank |
| 第 10 週 | Inner product, length, distance and angle; orthogonal sets Application spotlight, e.g., cosine similarity & embeddings |
| 第 11 週 | 11/18 (Wednesday) 全校運動會: no class 11/20 (Friday) Review for Exam 2 |
| 第 12 週 | 11/25 (Wednesday) Exam #2 (weeks 6–10) Orthogonal projections |
| 第 13 週 | The Gram-Schmidt process Least-squares problems Application spotlight, e.g., linear regression |
| 第 14 週 | Symmetric matrices and orthogonal diagonalization Quadratic forms |
| 第 15 週 | The Singular Value Decomposition (SVD) Application spotlight, e.g., PCA, image compression, recommender systems |
| 第 16 週 | 12/23 (Wednesday) Exam #3 (weeks 12–15) |
Steven J. Leon, Linear Algebra with Applications, 10th ed., Pearson. （The lecture sequence differs from the book's chapter order.） 【提醒~尊重智財權】 1. 請同學勿使用非法教科書 2. 請尊重與保護智慧財產權勿非法下載及影印有版權之檔案
- 地點
- EC332C
- 時間
- To be announced
- 聯絡方式
- po-kai.yang@nycu.edu.tw