Linear Algebra 2023 Fall



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Homework

# Date Topic TA Slides Video
HW0 Colab 承櫸, 鳴鐸 SLIDE VIDEO
HW1 9/22 - 10/4 Cycle Detection 承櫸, 鳴鐸 SLIDE VIDEO
HW2 10/06 - 11/03 Hill Cipher 品翔, 卓耀 SLIDE VIDEO
HW3 11/03 Transform and Its Application 冠廷, 元翔 SLIDE VIDEO
HW4 11/17 PageRank 元翔, 品翔 SLIDE VIDEO
HW5 12/01 Linear Regression 卓耀, 徐行 SLIDE VIDEO
HW6 12/15 SVD for Image Compression 鳴鐸, 承櫸
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Course Materials

✓  review 🔍  overview ★  basic concept ＋  optional
def.  definition ex.  example pf.  proof thm.  theorem
✓  review
🔍  overview
★  basic concept
＋  optional
def.  definition
ex.  example
pf.  proof
thm.  theorem
Chapter 1
DueDate Topic YouTube Textbook PDF PPT
1 linear
9/6 def. Linear System 1-1 1 - 4 1 - 4
9/6 ex. Are they Linear System? 1-2 5 - 7 5 - 7
9/6 ex. Derivative and Integral are Linear Systems 1-3 8 - 10 8 - 10
2 course introduction
yourself ＋ Linear Algebra v.s. Compulsory Courses (optional) 2 1 - 4 1 - 4
yourself ＋ Course Overview (optional) 3 1 - 6 1 - 6
3 vector
yourself ✓ Vector 4-1 1.1 PDF link PPT link
yourself ✓ Properties of Vector 4-2 1.1 PDF link PPT link
4 system of linear equations
9/13 ✓ System of Linear Equations 5-1 1.3 1 - 2 1 - 2
9/13 ★ System of Linear Equations = Linear System 5-2 1.3 3 - 6 3 - 6
5 matrix
9/13 ✓ Matrix 6-1 1.1 1 - 3 1 - 3
9/13 ✓ Properties of Matrix 6-2 1.1 4 - 5 4 - 5
9/13 def. Diagonal, Identity, Zero Matrix 7-1 1.2 1 - 2 1 - 2
9/13 def. Transpose 7-2 1.1 3 - 4 3 - 4
4 system of linear equations
9/13 ✓ Matrix-Vector Product 8-1 1.2 1 - 3 1 - 3
9/13 ★ Matrix-Vector Product = System of Linear Equations 8-2 1.2 4 - 5 4 - 5
9/13 ex. Matrix-Vector Product (Example) 8-3 1.2 6 6
9/13 ★ Properties of Matrix-Vector Product 9-1 1.2 1 - 3 1 - 3
9/13 ★ Standard Vector 9-2 1.2 4 4
6 solution
9/13 ✓ Solution of System of Linear Equations (high school) 10 1.3 1 - 4 1 - 4
9/13 🔍 Solution of System of Linear Equations (this course) 11 5 - 7 5 - 7
9/13 def. Linear Combination 12-1 1.2 1 - 2 1 - 2
9/13 ★ Linear Combination v.s. Solution 12-2 1.2 3 - 4 3 - 4
9/13 ex. Linear Combination v.s. Solution (Example 1) 12-3 1.2 5 - 6 5 - 6
9/13 ex. Linear Combination v.s. Solution (Example 2) 12-4 1.2 7 - 9 7 - 9
9/13 ex. Linear Combination v.s. Solution (Example 3) 12-5 1.2 10 - 12 10 - 12
9/13 def. Span 13-1 1.6 1 - 2 1 - 2
9/13 ex. Span (Example) 13-2 1.6 3 - 6 3 - 6
9/13 ★ Span v.s. Solution 13-3 1.6 7 - 9 7 - 9
9/13 thm. Span (Theorem of Useless Vector) 14-1 1.6 1 - 3 1 - 3
9/13 pf. Span (Theorem of Useless Vector) 14-2 1.6 3 - 4 3 - 4
9/20 ＋ Exercise 1.6 Video PDF PTT
9/20 def. Dependent / Independent 15-1 1.7 1 - 2 1 - 2
9/20 ex. Dependent / Independent (Example) 15-2 1.7 3 - 5 3 - 5
9/20 ★ Dependent / Independent (Intuitive Explaination) 15-3 1.7 6 - 8 6 - 8
9/20 ★ Dependent / Independent v.s. Solution 15-4 1.7 9 9
9/20 ex. Dependent / Independent v.s. Solution (Example) 15-5 1.7 10 10
9/20 def. Dependent / Independent (Another Definition) 15-6 1.7 11 - 12 11 - 12
9/20 pf. Dependent / Independent v.s. Solution (Proof) 15-7 1.7 13 13
9/20 ＋ Exercise 1.7 Video   PDF PTT
9/20 ＋ Exercise 1.7.2 Video   PDF PPT
9/20 def. Rank / Nullity 16-1 1 - 2 1 - 2
9/20 ex. Rank / Nullity (Example 1) 16-2 3 3
9/20 ex. Rank / Nullity (Example 2) 16-3 4 4
9/20 ex. Rank / Nullity (Example 3) 16-4 5 5
9/20 ★ Rank / Nullity v.s. Solution 16-5 6 6
9/20 ＋ Story of Gaussian Elimination (optional) 17 1.4 PDF link PPT link
9/20 ★ Strategy of Finding Solutions 18-1 1.4 1 - 5 1 - 5
9/20 ★ Elementary Row Operation 18-2 1.4 6 - 11 6 - 11
9/20 def. REF 19-1 1.4 1 - 4 1 - 4
9/20 def. RREF 19-2 1.4 5 - 6 5 - 6
9/20 def. Pivot Columns 19-3 1.4 7 7
9/20 thm. RREF is unique 19-4 1.4 8 8
9/20 ★ RREF v.s. unique solution 20-1 1.4 1 - 3 1 - 3
9/20 ★ RREF v.s. infinite solutions 20-2 1.4 4 4
9/20 ★ RREF v.s. no solution 20-3 1.4 5 5
9/20 ~~~~~~ HW1 Released! ~~~~~~ Go to...
9/27 ex. Find RREF (Example 1) 21-1 1.4 1 - 8 1 - 8
9/27 ex. Find RREF (Example 1) - Find solution 21-2 1.4 9 - 10 9 - 10
9/27 ex. Find RREF (Example 2) 21-3 1.4 11 11
9/27 ex. Find RREF (Example 3) 21-4 1.4 12 - 13 12 - 13
9/27 ＋ Exercise 1.4 Video   PDF PPT
7 RREF
9/27 thm. Column Correspondence Theorem 22-1 1 - 4 1 - 4
9/27 ★ Column Correspondence Theorem - Reason 1 22-2 5 5
9/27 thm. Ax = 0 and Rx = 0 are equivalent 22-3 6 - 8 6 - 8
9/27 ★ Column Correspondence Theorem - Reason 2 22-4 9 - 10 9 - 10
9/27 ★ No Row Correspondence Theorem 22-5 11 11
9/27 ★ How to Check Independence 23-1 1.7 1 - 5 1 - 5
9/27 ★ Independence v.s. Column Correspondence Theorem 23-2 1.7 6 - 7 6 - 7
9/27 ★ Independence v.s. Matrix Size 23-3 1.7 8 - 12 8 - 12
9/27 def. Rank = no. of Pivot Columns = no. of non-zero rows in RREF 24-1 1.7 1 - 2 1 - 2
9/27 ★ Independence v.s. Matrix Size (again) 24-2 1.7 3 - 5 3 - 5
9/27 def. Rank v.s. Basic / Free Variables 24-3 1.7 6 6
9/27 🔍 Definitions of Rank and Nullity 24-4 1.7 7 7
9/27 ★ All properties about always consistent 25-1 1.7 1 - 4 1 - 4
9/27 thm. More than m vectors in Rm must be dependent 25-2 1.7 5 - 8 5 - 8
9/27 ＋ Three is a powerful number :) (optional) 25-3 1.7 9 9
Chapter 2
DueDate Topic YouTube Textbook PDF PPT
1 matrix multiplication
9/27 ✓ Matrix Multiplication: inner product 26-1 2.1 1 - 6 1 - 6
9/27 ★ Matrix Multiplication: Combination of Columns 26-2 2.1 7 - 9 7 - 9
9/27 ★ Matrix Multiplication: Combination of Rows 26-3 2.1 10 - 12 10 - 12
9/27 ★ Matrix Multiplication: Summation of Matrices 26-4 2.1 13 - 15 13 - 15
9/27 ★ Block Multiplication 26-5 2.1 16 - 18 16 - 18
9/27 ex. Block Multiplication - Example 26-6 2.1 19 - 20 19 - 20
9/27 ★ Matrix Multiplication means multiple inputs 27-1 2.1 1 - 2 1 - 2
9/27 ★ Matrix Multiplication represents Composition 27-2 2.1 3 - 7 3 - 7
9/27 ex. Matrix Multiplication represents Composition - Example 27-3 2.1 8 - 9 8 - 9
10/ 4 ★ Matrix Multiplication - Properties 28-1 2.1 1 - 4 1 - 4
10/ 4 ★ Matrix Multiplication - Transpose 28-2 2.1 5 - 6 5 - 6
10/ 4 ＋ Matrix Multiplication - Pratical Computation Issue (optional) 28-3 2.1 7 - 8 7 - 8
10/ 4 ＋ Exercise 2.1 Video PDF PPT
2 matrix inverse
10/ 4 def. Inverse of Matrix 29-1 2.4 1 - 4 1 - 4
10/ 4 ★ Inverse of Matrix - Properties 29-2 2.4 5 - 6 5 - 6
10/ 4 ★ Inverse of Matrix - Matrix Transpose 29-3 2.4 8 8
10/ 4 ★ Inverse of Matrix - Matrix Multiplication 29-4 2.4 7 7
10/ 4 ＋ Inverse of Matrix - Solving System of Linear Equations (optional) 30-1 2.4 1 - 2 1 - 2
10/ 4 ＋ Inverse of Matrix - Input-output Model 1 (optional) 30-2 2.4 3 - 5 3 - 5
10/ 4 ＋ Inverse of Matrix - Input-output Model 2 (optional) 30-3 2.4 6 6
10/ 4 thm. Invertible Matrix Theorem 31-1 2.4 1 - 3 1 - 3
10/ 4 ✓ Review: one-to-one and onto 31-2 2.8 4 - 5 4 - 5
10/ 4 ★ One-to-one in Linear Algebra 31-3 2.8 6 6
10/ 4 ★ Onto in Linear Algebra 31-4 2.8 7 7
10/ 4 ★ Invertible = One-to-one and Onto 31-5 2.8 8 - 10 8 - 10
10/ 4 pf. Invertible Matrix Theorem - Proof (part 1) 32-1 2.4 1 - 5 1 - 5
10/ 4 pf. Invertible Matrix Theorem - Proof (part 2) 32-2 2.4 6 - 8 6 - 8
10/ 4 def. Elementary Matrix 33-1 2.3 1 - 5 1 - 5
10/ 4 ＋ Exercise 2.3 Video PDF PPT
10/ 4 ★ Inverse of Elementary Matrix 33-2 2.3 6 6
10/ 4 pf. Invertible Matrix Theorem - Proof (part 3) 33-3 2.4 7 - 8 7 - 8
10/ 4 ＋ Find A-1 (Special Case: 2x2 matrices) (optional) 34-1 2.4 1 - 2 1 - 2
10/ 4 ★ Find A-1 34-2 2.4 3 - 5 3 - 5
10/ 4 ★ Find A-1C 34-3 2.4 6 6
10/ 4 ＋ Exercise 2.4 Video 1 2 PDF PPT
10/ 4 ~~~~~~ HW1 Due! ~~~~~~ Go to...
10/ 4 ~~~~~~ HW2 Released! ~~~~~~ Go to...
Chapter 4-(1)
DueDate Topic YouTube Textbook PDF PPT
  subspace
10/ 11 def. Subspace 35-1 4.1 1 - 3 1 - 3
10/ 11 ex. Subspace - Example 35-2 4.1 4 4
10/ 11 ★ Subspace v.s. Span 35-3 4.1 5 5
10/ 11 ＋ Exercise 4.1-1 Video PDF PPT
10/ 11 ＋ Exercise 4.1-2 Video 1 2 PDF PPT
10/ 11 def. Column Space and Row Space 35-4 4.3 6 - 9 6 - 9
10/ 11 def. Null Space 35-5 4.3 10 - 11 10 - 11
10/ 11 def. Basis 36-1 4.2 1 - 2 1 - 2
10/ 11 ex. Basis - Example 36-2 4.2 3 3
10/ 11 thm. More Theorems of Span 36-3 4.2 4 4
10/ 11 thm. Three Theorems of Basis 36-4 4.2 5 5
10/ 11 def. Dimension 36-5 4.2 6 - 8 6 - 8
10/ 11 ★ More than m vectors in Rm must be dependent (again and again) 36-6 4.2 9 - 12 9 - 12
10/ 11 pf. Proof of Basis Theorem 1 - Reduction Theorem 36-7 4.2 13 - 15 13 - 15
10/ 11 pf. Proof of Basis Theorem 2 - Extension Theorem 36-8 4.2 16 - 17 16 - 17
10/ 11 pf. Proof of Basis Theorem 3 - Dimension 36-9 4.2 18 18
10/ 11 thm. Dimension v.s. "Size" of Subspace 37-1 4.3 19 19
10/ 11 🔍 Three Theorems of Basis (review) 37-2 4.2 20 - 21 20 - 21
10/ 11 ★ Is it a basis? - Based on Definition 38-1 4.2 1 - 2 1 - 2
10/ 11 ★ Is it a basis? - Easier Way 38-2 4.2 3 - 4 3 - 4
10/ 11 ex. Is it a basis? - Example 38-3 4.2 5 - 6 5 - 6
10/ 11 ＋ Exercise 4.2 Video PDF PPT
10/ 11 ★ Basis and Dimension of Column Space (More definitions of Rank!) 39-1 4.3 1 - 3 1 - 3
10/ 11 ★ Basis and Dimension of Row Space (More definitions of Rank!) 39-2 4.3 4 - 5 4 - 5
10/ 11 thm. Rank A = Rank AT !!! 39-3 4.3 6 6
10/ 11 ★ Basis and Dimension of Null Space 39-4 4.3 7 - 8 7 - 8
10/ 11 thm. Dimension Theorem 39-5 4.3 9 9
10/ 18 ＋ Exercise 4.3-1 Video 1 2 PDF PPT
10/ 18 ＋ Exercise 4.3-2 Video PDF PPT
Chapter 3
DueDate Topic YouTube Textbook PDF PPT
  determinant
10/ 18 ＋ Determinant (high school) (optional) 44-1 3.1 1 - 2 1 - 2
10/ 18 def. Determinant - Cofactor Expansion 44-2 3.1 3 - 5 3 - 5
10/ 18 ex. Determinant of 2x2 and 3x3 matrices 44-3 3.1 6 6
10/ 18 ex. Determinant of 2x2 and 3x3 matrices 44-4 3.1 7 7
10/ 18 ＋ Determinant of a special gigantic matrix (optional) 44-5 3.1 8 - 11 8 - 11
10/ 18 def. Three Basic Properties of Determinant 45-1 1 - 3 1 - 3
10/ 18 ★ Basic Property 1 45-2 4 4
10/ 18 ★ Basic Property 2 45-3 5 - 6 5 - 6
10/ 18 ★ Basic Property 3 45-4 7 - 11 7 - 11
10/ 18 ＋ From Basic Properties to Cofactor Expansion (2x2 matrix) (optional) 45-5 12 - 13 12 - 13
10/ 18 ＋ From Basic Properties to Cofactor Expansion (3x3 matrix) (optional) 45-6 14 - 15 14 - 15
10/ 18 ＋ From Basic Properties to Cofactor Expansion (nxn matrix) (optional) 45-7 16 - 17 16 - 17
10/ 18 ＋ Formula of A-1 (optional) 46-1 1 - 2 1 - 2
10/ 18 ＋ Formula of A-1 - Example (optional) 46-2 3 3
10/ 18 ＋ Formula of A-1 - Proof (optional) 46-3 4 4
10/ 18 ＋ Cramer’s Rule (optional) 46-4 3.2 5 - 6 5 - 6
10/ 18 ＋ Three Basic Properties of Determinant (review) (optional) 47-1 3.2 1 - 3 1 - 3
10/ 18 thm. A is invertible = det (A) is not zero 47-2 3.2 4 - 5 4 - 5
10/ 18 ex. example 47-3 3.2 6 6
10/ 18 thm. Properties of Determinant 47-4 3.2 7 7
10/ 18 pf. det(AB) = det(A)det(B) 47-5 3.2 8 - 11 8 - 11
10/ 18 pf. det(A) = det (AT) 47-6 3.2 12 - 16 12 - 16
10/ 18 ＋ Chapter 3 Video PDF PPT
10/ 18 ＋ Review Video PDF PPT
Chapter 4-(2)
  subspace
11/ 1 def. Coordinate System 40-1 4.4 1 - 3 1 - 3
11/ 1 ex. Coordinate System - Example 40-2 4.4 4 4
11/ 1 ＋ 莊子齊物論 (optional) 40-3 4.4 5 - 8 5 - 8
11/ 1 def. Cartesian Coordinate System 40-4 4.4 9 9
11/ 1 ＋ 蓋亞思維 (optional) 40-5 4.4 9 9
11/ 1 ★ A coordinate system is a basis 40-6 4.4 10 - 11 10 - 11
11/ 1 ★ Other system to Cartesian 41-1 4.4 1 - 4 1 - 4
11/ 1 ★ Cartesian to Other system 41-2 4.4 5 5
11/ 1 ★ Change Coordinate 41-3 4.4 6 6
11/ 1 ＋ Equation of ellipse (optional) 42-1 4.4 7 - 9 7 - 9
11/ 1 ＋ Equation of hyperbola (optional) 42-2 4.4 10 - 12 10 - 12
11/ 1 ＋ Exercise 4.4 Video PDF PPT
11/ 1 ＋ 全面啟動 (optional) 43-1 4.5 1 - 4 1 - 4
11/ 1 ex. Describing a function in another coordinate system 43-2 4.5 5 - 8 5 - 8
11/ 1 ★ Function in Different Coordinate Systems 43-3 4.5 9 - 11 9 - 11
11/ 1 ex. Function in Different Coordinate Systems - Example 43-4 4.5 12 - 13 12 - 13
11/ 1 ex. Function in Different Coordinate Systems - Example 43-5 4.5 14 - 17 14 - 17
11/ 1 ＋ Exercise 4.5 Video PDF PPT
11/ 1 ~~~~~~ HW2 Due! ~~~~~~ Go to...
11/ 1 ~~~~~~ HW3 Released! ~~~~~~ Go to...
Chapter 5
DueDate Topic YouTube Textbook PDF PPT
  eigenvalues and eigenvectors
11/11 ＋ How to find a "good" coordinate system? (optional) 48-1 5.1 1 - 2 1 - 2
11/11 def. Eigenvalues and Eigenvectors 48-2 5.1 3 - 6 3 - 6
11/11 ex. Example 48-3 5.1 7 - 10 7 - 10
11/11 ★ Do the eigenvectors correspond to an eigenvalue from a subspace? 48-4 5.1 11 - 13 11 - 13
11/11 def. Eigenspace 48-5 5.1 14 14
11/11 ★ Check whether a scalar is an eigenvalue 48-6 5.1 15 - 16 15 - 16
11/11 ex. Example 48-7 5.1 17 - 18 17 - 18
11/11 ★ Looking for Eigenvalues 48-8 5.1 19 - 20 19 - 20
11/11 ex. Looking for Eigenvalues - Example 1 48-9 5.1 21 - 22 21 - 22
11/15 ex. Looking for Eigenvalues - Example 2 49-1 5.1 23 23
11/15 ex. Looking for Eigenvalues - Example 3 49-2 5.1 24 24
11/15 ＋ Exercise 5.1 Video (former half) PDF PPT
11/15 def. Characteristic Polynomial 49-3 5.2 25 25
11/15 ★ Matrix A and RREF of A have different eigenvalues 49-4 5.2 26 26
11/15 thm. Similar matrices have the same eigenvalues 49-5 5.2 26 26
11/15 thm. More Properties of Characteristic Polynomial 49-6 5.2 27 - 30 27 - 30
11/15 ＋ Exercise 5.2-1 Video (latter half) PDF PPT
11/15 ＋ Exercise 5.2-2 Video 1 2 PDF
11/15 ＋ PageRank: How does Google rank search results? (optional) 50-1 1 - 3 1 - 3
11/15 ＋ PageRank: Introduction (optional) 50-2 4 - 7 4 - 7
11/15 ＋ PageRank: Basic Idea (optional) 50-3 8 - 10 8 - 10
11/15 ＋ PageRank: Formulation (optional) 50-4 11 11
11/15 ＋ PageRank: Relation to Eigenvectors / Eigenvalues (optional) 50-5 12 - 13 12 - 13
11/15 ＋ PageRank: Always having eigenvalue = 1 (optional) 50-6 14 14
11/15 ＋ PageRank: When does dimension of eigenspace = 1 (optional) 50-7 15 - 17 15 - 17
11/15 ＋ PageRank: How to make dimension of eigenspace = 1 (optional) 50-8 18 18
11/15 ＋ PageRank: Power Method (optional) 50-9 19 19
11/15 ~~~~~~ HW3 Due! ~~~~~~ Go to...
11/15 ~~~~~~ HW4 Released! ~~~~~~ Go to...
11/15 def. Diagonalizable 51-1 5.3 1 - 4 1 - 4
11/15 ★ Not all matrices are diagonalizable 51-2 5.3 5 5
11/15 ★ How to diagonalize a matrix 51-3 5.3 6 - 8 6 - 8
11/15 thm. Eigenvectors corresponding to distinct Eigenvalues is independent 51-4 5.3 9 - 10 9 - 10
11/15 ★ Find independent eigenvectors 52-1 5.3 11 11
11/15 ex. Example 52-2 5.3 12 12
11/15 ★ Test for Diagonalizable Matrix 52-3 5.3 13 - 14 13 - 14
11/15 ＋ Application of Diagonalization 1: 這就是人生! (optional) 52-4 5.3 15 15
11/15 ＋ Application of Diagonalization 1: 你花了多少時間在念線性代數? (optional) 52-5 5.3 15 - 18 15 - 18
11/15 ex. Diagonalization of Linear Operator 52-6 5.3 19 - 20 19 - 20
11/15 ★ Application of Diagonalization 2: Find a good Coordinate System 52-7 5.3 21 - 26 21 - 26
11/22 ＋ Exercise 5.3 Video 1 2 PDF
11/22 ＋ Chapter 5 Video 1 2 PDF
Chapter 7
DueDate Topic YouTube Textbook PDF PPT
  orthogonality
11/22 def. Norm and Distance 53-1 7.1 1 - 3 1 - 3
11/22 def. Dot Product and Orthogonal 53-2 7.1 4 - 7 4 - 7
11/22 thm. Pythagorean Theorem 53-3 7.1 8 8
11/22 thm. Dot Product v.s. Geometry 53-4 7.1 9 9
11/22 thm. Triangle Inequality 53-5 7.1 10 - 11 10 - 11
11/22 def. Orthogonal Set 54-1 7.2 1 - 3 1 - 3
11/22 ★ Orthogonal Set v.s. Independent Set 54-2 7.2 4 4
11/22 def. Orthonormal Set 54-3 7.2 5 5
11/22 def. Orthogonal / Orthonormal Basis 54-4 7.2 6 6
11/22 thm. Orthogonal Decomposition Theory 54-5 7.2 7 - 8 7 - 8
11/22 ex. Example 54-6 7.2 9 9
11/22 thm. Gram-Schmidt Process 54-7 7.2 10 - 11 10 - 11
11/22 ex. Example 54-8 7.2 12 - 13 12 - 13
11/22 pf. Proof of Gram-Schmidt Process (1): Obtaining Orthogonal Set 54-9 7.2 14 14
11/22 pf. Proof of Gram-Schmidt Process (2): Obtaining Basis 54-10 7.2 15 15
11/22 def. Orthogonal Complement 55-1 7.3 1 - 4 1 - 4
11/22 ex. Example 55-2 7.3 4 - 5 4 - 5
11/22 thm. B be a basis of W, then B⟂ = W⟂ 55-3 7.3 6 - 7 6 - 7
11/22 ex. How to find W⟂ 55-4 7.3 8 8
11/22 thm. Orthogonal Complement v.s. Null Space 55-5 7.3 9 9
11/22 thm. u = w + z → w ∈ W, z ∈ W⟂ 55-6 7.3 10 10
11/29 def. Orthogonal Projection 56-1 7.4 11 - 13 11 - 13
11/29 thm. Closest Vector Property 56-2 7.4 14 14
11/29 def. Orthogonal Projection Matrix 56-3 7.3 15 15
11/29 ★ Orthogonal Projection on a line 57-1 7.3 16 - 18 16 - 18
11/29 thm. Orthogonal Projection Matrix 57-2 7.3 19 - 22 19 - 22
11/29 pf. Orthogonal Projection Matrix - Proof (part I) 57-3 7.3 19 19
11/29 pf. Orthogonal Projection Matrix - Proof (part II) 57-4 7.3 20 20
11/29 ★ Orthogonal Decomposition Theory v.s. Orthogonal Projection Matrix 57-5 7.3 23 - 24 23 - 24
11/29 ＋ Exercise 7.3 Video PDF PPT
11/29 ★ Applications of Orthogonal Projection 58-1 7.4 25 - 26 25 - 26
11/29 ★ Least Square Approximation - Problem Statement 58-2 7.4 27 27
11/29 ★ Least Square Approximation - Solving by Orthogonal Projection 58-3 7.4 28 - 30 28 - 30
11/29 ex. Least Square Approximation - Example 1 58-4 7.4 31 31
11/29 ex. Least Square Approximation - Example 2 58-5 7.4 32 - 34 32 - 34
11/29 ex. Least Square Approximation - Example 3 58-6 7.4 35 35
12/ 6 ＋ Exercise 7.4 Video (former half) PDF PPT
11/29 def. Orthogonal Matrix 59-1 7.5 1 - 3 1 - 3
11/29 def. Norm-preserving 59-2 7.5 4 - 5 4 - 5
11/29 ★ Orthogonal Matrix = Norm-preserving 59-3 7.5 6 6
11/29 thm. Properties of Orthogonal Matrix 59-4 7.5 7 7
11/29 pf. Properties of Orthogonal Matrix - Proof 59-5 7.5 8 8
11/29 thm. det Q, PQ, Q⁻¹, Qᵀ 59-6 7.5 9 9
11/29 ＋ Orthogonal Operator (optional) 59-7 7.5 10 - 12 10 - 12
12/ 6 ＋ Exercise 7.5 Video (latter half) PDF PPT
12/ 6 ~~~~~~ HW4 Due! ~~~~~~ Go to...
12/ 6 ~~~~~~ HW5 Released! ~~~~~~ Go to...
12/ 6 ★ symmetric matrices: eigenvalues are always real (2x2 matrices) 60-1 7.6 13 - 14 13 - 14
12/ 6 thm. symmetric matrices: eigenvalues are always real (general cases) 60-2 7.6 15 15
12/ 6 thm. symmetric matrices: eigenvectors for different eigenvalues are orthogonal 60-3 7.6 16 - 17 16 - 17
12/ 6 thm. symmetric matrices are diagonalizable 60-4 7.6 18 18
12/ 6 pf. symmetric matrices are diagonalizable (proof I) 60-5 7.6 19 19
12/ 6 pf. symmetric matrices are diagonalizable (proof II) 60-6 7.6 20 - 21 20 - 21
12/ 6 ex. symmetric matrices are diagonalizable (example) 60-7 7.6 22 22
12/ 6 ex. symmetric matrices are diagonalizable (example) 60-8 7.6 23 23
12/ 6 ★ How to diagonalize symmetric matrices 60-9 7.6 24 - 25 24 - 25
12/ 6 thm. Spectral Decomposition 60-10 7.6 26 - 27 26 - 27
12/ 6 ex. Spectral Decomposition (example) 60-11 7.6 28 28
12/ 6 ＋ Singular Value Decomposition (SVD) (optional) 61-1 7.7 1 - 3 1 - 3
12/ 6 ＋ SVD v.s. Rank (optional) 61-2 7.7 4 4
12/ 6 ＋ SVD - Low Rank Approximation (optional) 61-3 7.7 5 - 6 5 - 6
12/ 6 ＋ SVD - Application (optional) 61-4 7.7 7 - 9 7 - 9
12/ 6 ＋ SVD - proof I (optional) 61-5 7.7 10 10
12/ 6 ＋ SVD - proof II (optional) 61-6 7.7 11 11
12/ 6 ＋ SVD - proof III (optional) 61-7 7.7 12 12
Chapter 6
DueDate Topic YouTube Textbook PDF PPT
  vector space
12/ 6 ★ 原來萬物都是 vector ! 62-1 6.1 1 - 5 1 - 5
12/ 6 def. Vector Space 62-2 6.1 6 - 8 6 - 8
12/ 6 ★ Revisit Subspace 62-3 6.1 9 - 11 9 - 11
12/ 6 ★ Revisit Linear Combination and Span 62-4 6.2 12 - 14 12 - 14
12/ 6 ~~~~~~ HW6 Released! ~~~~~~ Go to...
12/ 13 ★ Revisit Linear Transformation 63-1 6.2 15 - 19 15 - 19
12/ 13 ★ Isomorphism 63-2 6.2 20 - 21 20 - 21
12/ 13 ★ Revisit Basis 63-3 6.3 22 - 25 22 - 25
12/ 13 ★ Vector Representation of Object 63-4 6.4 26 26
12/ 13 ★ Matrix Representation of Linear Operator 63-5 6.4 27 - 31 27 - 31
12/ 13 ★ Revisit Eigenvalue and Eigenvector 63-6 6.4 32 - 35 32 - 35
12/ 13 def. Inner Product 64-1 6.5 36 - 37 36 - 37
12/ 13 ex. Example 64-2 6.5 38 - 39 38 - 39
12/ 13 ★ Revisit Orthogonal/Orthonormal Basis 64-3 6.5 40 - 41 40 - 41
12/ 13 ex. Example 64-4 6.5 42 - 44 42 - 44
12/27 ~~~~~~ HW5 Due! ~~~~~~ Go to...
12/27 ~~~~~~ HW6 Due! ~~~~~~ Go to...
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2023 ESSENCE

Topic
9/06(三) 課程規則說明
9/08(五) 沒有上課
9/15(五) 沒有上課
9/22(五) 公告作業一
9/29(五) 放假
10/06(五) 公告作業二
10/13(五) 期中考複習
10/20(五) 期中考複習
10/27(五) 期中考
11/03(五) 公告作業三
11/10(五) 80分鐘快速全面了解大型語言模型 (PPTX)
11/17(五) 公告作業四
11/24(五) 校慶停課
12/01(五) 公告作業五
12/08(五) 期末考複習
12/15(五) 公告作業六
12/22(五) 期末考