線性代數
Linear Algebra
學期
113-2
學分
3
學分
當期課號
515403
永久課號
EEDP10016
開課單位
光電工程學系
授課教師
田仲豪
校區
光復
類別
必修
上課時間表
| 節 | 週二 | 週四 |
|---|---|---|
2 09:00–09:50 | 線性代數 CY202 | |
5 13:20–14:10 | 線性代數 CY202 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
概述
線性系統、矩陣與向量分析、特徵值與特徵向量
先修科目
無
教學方式
4.教學方法及教學相關配合事項(如網站、助教、圖書講義及資料庫等):e3 system
評分方式
1學期作業:無 2.考試狀況:Quiz #6 (60%), med-term (20%), final (20%)
課程大綱
- Introduction to Linear Algebra (1) The Geometry of Linear Equations (2.1)
- Elimination (2.2) Matrix Operation Elimination using Matrices (2.3)
- Rule of Matrix Multiplication (2.4) Inverse Matrices (2.5)
- Factorization A = LU (2.6) Transposes and Permutations (2.7)
- Vector Spaces (3.1)
- Column Space C(A) and Null Space N(A) (3.2)
- Rank and the RREF (3.3)
- Complete Solution (3.4)
- Independence, Basis and Dimension (3.5)
- 4 fundamental subspaces (3.6)
- Bases of new vector spaces Rank one Matrices Small World Graphs
- Applications
- Orthogonal vectors and subspace (4.1)
- Projection (4.2)
- Least square approximation (4.3)
- Orthogonal Bases and Gram-Schmidt (4.4)
- Determinants (5.1)
- Permutations and cofactors (5.2)
- Cramer’s rule, Inversion and Volumes (5.3)
- Eigenvalues and Eigenvectors (6.1)
- Diagonalizing a Matrix (6.2)
- Differential Equations (6.3)
- Markov Matrices (8.3) and Fourier Series (8.5)
- Symmetric matrices (6.4)
- Complex vectors of Matrices (10)
- Positive Definite Matrices (6.5)
- Similar Matrices (6.6)
- Singular Value Decomposition (SVD) (6.7)
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction to Linear Algebra The Geometry of Linear Equations (1, 2.1)Elimination (2.2)Matrix Operation Elimination using Matrices (2.3) |
| 第 2 週 | Rule of Matrix Multiplication (2.4) Inverse Matrices (2.5)Factorization A = LU (2.6)Transposes and Permutations (2.7)Quiz#1 Chap. 1-2 |
| 第 3 週 | Vector Spaces (3.1)Column Space C(A) and Null Space N(A) (3.2) |
| 第 4 週 | Rank and the RREF (3.3)Complete Solution (3.4) |
| 第 5 週 | Independence, Basis and Dimension (3.5) |
| 第 6 週 | 4 fundamental subspaces (3.6)Bases of new vector spacesRank one MatricesSmall World Graphs |
| 第 7 週 | ApplicationsQuiz#2 Chap. 3Orthogonal vectors and subspace (4.1) |
| 第 8 週 | Projection (4.2)Least square approximation (4.3)Quiz#3 Chap. 4.1-4.3 |
| 第 9 週 | Orthogonal Bases and Gram-Schmidt (4.4) Mid-term |
| 第 10 週 | Determinants (5.1)& ampamp#9Permutations and cofactors (5.2) |
| 第 11 週 | Cramer’s rule, Inversion and Volumes (5.3)Quiz#4 Chap. 5 |
| 第 12 週 | Eigenvalues and Eigenvectors (6.1)Diagonalizing a Matrix (6.2) |
| 第 13 週 | Differential Equations (6.3)Markov Matrices (8.3) and Fourier Series (8.5) Quiz#5 Chap. 6.1-6.3 |
| 第 14 週 | Symmetric matrices (6.4)Complex vectors of Matrices (10) |
| 第 15 週 | Positive Definite Matrices (6.5)Quiz#6 Chap. 6.4-6.5 |
| 第 16 週 | Similar Matrices (6.6) |
| 第 17 週 | Singular Value Decomposition (SVD) (6.7) |
| 第 18 週 | Final |
教科書
Gilbert Strang, Introduction to Linear Algebra.