線性代數
Linear Algebra
| 節 | 週二 | 週四 |
|---|---|---|
2 09:00–09:50 | 線性代數 CY202（光復） | |
5 13:20–14:10 | 線性代數 CY202（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
線性系統、矩陣與向量分析、特徵值與特徵向量
無
無備註
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
1學期作業:無 2.考試狀況:Quiz #6 (60%), med-term (20%), final (20%)
Introduction to Linear Algebra (1) The Geometry of Linear Equations (2.1)
row picture column picture matrix form in linear equation
Elimination (2.2) Matrix Operation Elimination using Matrices (2.3)
idea of elimination; back substitution row/column operation row reduction for elimination
Rule of Matrix Multiplication (2.4) Inverse Matrices (2.5)
Matrix-vector operation 4 ways to see the matrix multiplication inverse Gauss-Jordan Elimination
Factorization A = LU (2.6) Transposes and Permutations (2.7)
production of elimination matrices matrix factorization (LU) RTR and RRT; PT=P-1
Vector Spaces (3.1)
Rn space; vector, linear combination, space, subspace, matrix form C(A)
Column Space C(A) and Null Space N(A) (3.2)
Ax = b and Ax = 0
Rank and the RREF (3.3)
computing nullspace (Ax = 0) pivot number (rank); free variables special solutions rref(A) = R
Complete Solution (3.4)
Ax= b; x= xp+xn; Matrix analyses (4 full rank cases)
Independence, Basis and Dimension (3.5)
Linear independence; spanning a space; basis for a vector space; dimension
4 fundamental subspaces (3.6)
Bases of new vector spaces Rank one Matrices Small World Graphs
Applications
Graphs and Networks Incidence matrix KCL
Orthogonal vectors and subspace (4.1)
Orthogonal vectors Subspace Row space orthogonal to nullspace Why projection Ax = b no solution
Projection (4.2)
Projection Projection matrix in 1D Why projection Ax = b no solution in 2D
Least square approximation (4.3)
Projection matrix Great picture Least square approximation ATA invertible (4G)
Orthogonal Bases and Gram-Schmidt (4.4)
Orthogonal bases Orthogonal matrix Q Gram-Schmidt A Q Factorization A = QR
Determinants (5.1)
10 properties
Permutations and cofactors (5.2)
Formula for detA Big formula Cofactors formula Special Tridiagonal matrices
Cramer’s rule, Inversion and Volumes (5.3)
Eigenvalues and Eigenvectors (6.1)
det[A-I] = 0 Trace = 1+2+... Determinant = 12...
Diagonalizing a Matrix (6.2)
A = SS-1 Power of A Fibonacci numbers
Differential Equations (6.3)
eAt of a matrix
Markov Matrices (8.3) and Fourier Series (8.5)
Markov Matrices (probability) Fourier Series (orthogonal projection)
Symmetric matrices (6.4)
A = QQT
Complex vectors of Matrices (10)
Complex inner product Hermitian and Unitary
Positive Definite Matrices (6.5)
Tests of positive matrix Minimum xTAx > 0 Ellipse equation ATA
Similar Matrices (6.6)
B = M-1AM
Singular Value Decomposition (SVD) (6.7)
A = UVT
| 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) 2023-02-14(二),2023-02-16(四) |
| 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 2023-02-21(二),2023-02-23(四) |
| 第 3 週 | Vector Spaces (3.1)Column Space C(A) and Null Space N(A) (3.2) 2023-02-28(二),2023-03-02(四) |
| 第 4 週 | Rank and the RREF (3.3)Complete Solution (3.4) 2023-03-07(二),2023-03-09(四) |
| 第 5 週 | Independence, Basis and Dimension (3.5) 2023-03-14(二),2023-03-16(四) |
| 第 6 週 | 4 fundamental subspaces (3.6)Bases of new vector spacesRank one MatricesSmall World Graphs 2023-03-21(二),2023-03-23(四) |
| 第 7 週 | ApplicationsQuiz#2 Chap. 3Orthogonal vectors and subspace (4.1) 2023-03-28(二),2023-03-30(四) |
| 第 8 週 | Projection (4.2)Least square approximation (4.3)Quiz#3 Chap. 4.1-4.3 2023-04-04(二),2023-04-06(四) |
| 第 9 週 | Orthogonal Bases and Gram-Schmidt (4.4) Mid-term 2023-04-11(二),2023-04-13(四) |
| 第 10 週 | Determinants (5.1)& #9 Permutations and cofactors (5.2) 2023-04-18(二),2023-04-20(四) |
| 第 11 週 | Cramer’s rule, Inversion and Volumes (5.3)Quiz#4 Chap. 5 2023-04-25(二),2023-04-27(四) |
| 第 12 週 | Eigenvalues and Eigenvectors (6.1)Diagonalizing a Matrix (6.2) 2023-05-02(二),2023-05-04(四) |
| 第 13 週 | Differential Equations (6.3)Markov Matrices (8.3) and Fourier Series (8.5) Quiz#5 Chap. 6.1-6.3 2023-05-09(二),2023-05-11(四) |
| 第 14 週 | Symmetric matrices (6.4)Complex vectors of Matrices (10) 2023-05-16(二),2023-05-18(四) |
| 第 15 週 | Positive Definite Matrices (6.5)Quiz#6 Chap. 6.4-6.5 2023-05-23(二),2023-05-25(四) |
| 第 16 週 | Similar Matrices (6.6) 2023-05-30(二),2023-06-01(四) |
| 第 17 週 | Singular Value Decomposition (SVD) (6.7) 2023-06-06(二),2023-06-08(四) |
| 第 18 週 | Final 2023-06-13(二),2023-06-15(四) |
Gilbert Strang, Introduction to Linear Algebra.
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