Linear Algebra 2021 Fall



Common Website Class Website NTU COOL
Go to today! ✈️    Go to homework! ✈️

Exercises

DueDate Topic YouTube PDF  PPT 
10/ 1 Exercise 1.6 (Oct. 1) Video PDF PPT
10/ 1 Exercise 1.7 (Oct. 1) Video PDF PPT
10/ 8 Exercise 1.7.2 (Oct. 8) Video PDF PPT
10/ 8 Exercise 1.4 (Oct. 8) Video PDF PPT
10/ 8 Exercise 2.1 (Oct. 8) Video PDF PPT
10/15 Exercise 2.1 (Oct. 15) Video PDF PPT
10/15 Exercise 2.3 (Oct. 15) Video PDF PPT
10/22 Exercise 2.4 (Oct. 22) Video 1 2 PDF PPT
10/22 Exercise 4.1 (Oct. 22) Video PDF PPT
10/29 Exercise 4.1 (Oct. 29) Video 1 2 PDF PPT
10/29 Exercise 4.2 (Oct. 29) Video PDF PPT
10/29 Exercise 4.3 (Oct. 29) Video 1 2 PDF PPT
11/ 5 Exercise 4.3 (Nov. 5) Video PDF PPT
11/ 5 Chapter 3 (Nov. 5) Video PDF PPT
11/ 5 Review (Nov. 5) Video PDF PPT
11/19 Exercise 4.4 (Nov. 19) Video PDF PPT
11/19 Exercise 4.5 (Nov. 19) Video PDF PPT😢
11/26 Exercise 5.1 (Nov. 26) Video (former half) PDF PPT
11/26 Exercise 5.2 (Nov. 26) Video (latter half) PDF PPT
12/10 Exercise 5.2 (Dec. 10) Video 1 2 PDF
12/10 Exercise 5.3 (Dec. 10) Video 1 2 PDF
12/10 Chapter 5 (Dec. 10) Video 1 2 PDF
12/17 Exercise 7.3 (Dec. 17) Video PDF PPT
12/24 Exercise 7.4 (Dec. 24) Video (former half) PDF PPT
12/24 Exercise 7.5 (Dec. 24) Video (latter half) PDF PPT

😢  : Sorry for missing some handwriting.
🚧  : Under construction.



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

Homework

# Date Topic TA Slides Video
10/ 1 Colab Tutorial 陳建成 Slides Video
HW110/ 1 Cycle Detection 林泓均 Slides Video
HW210/15 Hill Cipher 劉聿珉 Slides Video
HW311/ 5 Cosine Transform and Its Application 林冠廷 Slides Video
HW411/26 PageRank 翁茂齊 Slides Video (original)
HW512/17 Linear Regression 陳建成 Slides Video
HW6 1/14 SVD for Image Compression 王凡林 Slides Video
Note: 🚧  implies the material is not available now.