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Udemy線上課程 線性代數 (Linear Algebra) (含教材) 講師:Wilson Ren 影音教學 中文發音 繁體中文字幕版(2DVD)

內容說明:
接近40小時的線性代數課程，帶你一步步學會線性代數的重要觀念和公式，趕快收藏起來!!

線性代數為電腦科學、資訊工程等領域的必修課程，其應用之廣泛，包含機器學習、深度學習、預測模型、電腦圖形處理以及加密系統等等。這堂線性代數課程內容包含基本的線性方程組的基本運算、向量空間、線性獨立、矩陣的可逆性、行列式、施特拉森演算法、線性轉換、還有特徵矩陣以及特徵值的尋找，一步一步帶你認識所有重要的觀念、證明、運算過程與題目解答。不論你的數學基礎為何，都可以有系統性的認識線性代數中的重要理論、公式與計算原理。所有課程中所提到的公式與定理皆有證明過程與對應例子，讓學習有紮實基礎!

另外，課程也包含線性代數在電腦科學中的應用，包含密碼學的加密與解密演算法、圖形與向量處理、2D旋轉壓縮移動矩陣、3D旋轉矩陣、歐拉定理證明等等。這堂課程也包含每個章節的獨立練習題，讓你能夠衡量學習成效與得到充分練習的機會。
課程內容:
01 - Introduction to Linear Algebra
001 Personal Website.html
002 Learning Tips.html
003 Textbook Use.html
004 Intro to Sets.mp4

02 - Linear Equations
005 Solving Linear Equations.mp4
006 Upper Triangular Form.mp4
007 Practice Solving Linear Equation System.mp4
008 Sum Up.mp4
009 1-1 Practice.html
009-Linear-Algebra-1-1-Homework.pdf
010 Homework Answer.mp4
011 Echelon Form.mp4
012 Reduced Row Echelon Form.mp4
013 Intro to Geogebra.mp4
014 RREF By Hand.mp4
015 RREF By Hand 2.mp4
016 Free and Basic Variables.mp4
017 Free and Basic Variables 2.mp4
018 (Optional) Deeper Understanding.mp4
019 Intro to Vector.mp4
020 Vector Addition.mp4
021 Scalar Multiplication and Vector Subtraction.mp4
022 134 Understand Vector Subtraction.mp4
023 Properties of Vectors.mp4
024 Linear Combinations.mp4
025 Span of Vectors.mp4
026 3Blue1Brown Video.html
027 Examples of Span.mp4
028 1-3 Practice.html
028-Linear-Algebra-1-3-Homework.pdf
029 1-3 Homework Answer.mp4
030 Matrix Vector Multiplication.mp4
031 Properties of Ax=b.mp4
032 Matrix Multiplication.mp4
033 1-4 Homework.html
033-Linear-Algebra-1-4-Homework.pdf
034 1-4 Homework Solution.mp4
035 Reach-ability Matrix.mp4
036 Homogeneous System.mp4
037 Homogeneous System 2.mp4
038 153 Nonhomogenous System.mp4
039 Chapter Review.mp4
040 1-5 Homework.html
040-Linear-Algebra-1-5-Homework.pdf
041 1-5 Homework Answer.mp4
042 Application of Linear System.mp4
043 Linear Independency.mp4
044 Linearly Dependent Set.mp4
045 Linearly Dependent Example.mp4
046 Idea of Linearly Independence.mp4
047 Tips on Solving Linear Independency problem.mp4
048 Linear Independence and Solution to Ax=b.mp4
049 1-7 Homework.html
049-Linear-Algebra-1-7-Homework.pdf
050 Homework Answer.mp4
051 Intro to Transformation.mp4
052 Definition of Linear Transformation.mp4
053 Uniqueness of Pre-image.mp4
054 1-8 Homework.html
054-Linear-Algebra-1-8-Homework.pdf
055 1-8 Homework Answer.mp4
056 Rotation Matrix.mp4
057 (Optional) Proof of Rotation Matrix.mp4
058 Finding Rotation Matrix.mp4
059 Finding Reflection Matrix for x-axis.mp4
060 Finding Reflection Matrix for y-axis.mp4
061 Finding Reflection Matrix for x=y.mp4
062 Finding Reflection Matrix for x=-y.mp4
063 Compound Reflection.mp4
064 Matrix for contraction and expansion.mp4
065 Matrix for Shear.mp4
066 Relations of Domain and Co-domain.mp4
067 Matrix for Transformation in General.mp4
068 Finding Matrix for Transformation.mp4
069 Finding Matrix for Transformation 2.mp4
070 Homework 1-9.html
070-Linear-Algebra-1-9-Homework.pdf
071 1-9 Homework Answer.mp4

03 - Matrix Algebra
072 Identity and Diagonal Matrix.mp4
073 Rules of Matrix Operations.mp4
074 Matrix Multiplication.mp4
075 Properties of Matrix Multiplication.mp4
076 Transpose of Matrix.mp4
077 2-1 Homework.html
077-Linear-Algebra-2-1-Homework.pdf
078 2-1 Homework Answer.mp4
079 Intro to Inverse Matrix.mp4
080 Inverse Matrix of 2x2 Matrix.mp4
081 Inverse Matrix for Solving Linear System.mp4
082 Properties of Inverse Matrix.mp4
083 Row Operations and the Corresponding Matrix.mp4
084 Gauss-Jordan Elimination of finding A inverse.mp4
085 Discussion of Inverse Matrix.mp4
086 Uniqueness of Inverse Matrix.mp4
087 Cost of Producing A Inverse.mp4
088 2-2 Homework.html
088-Linear-Algebra-2-2-Homework.pdf
089 2-2 Homework Answer.mp4
090 Characterization of Invertible Matrix.mp4
091 Examples of Invertible Matrix.mp4
092 2-3 Homework.html
092-Linear-Algebra-2-3-Homework.pdf
093 2-3 Homework Solution.mp4
094 (Optional) Poly-alphabetic Cryptosystem.mp4
095 Partitioned Matrix.mp4
096 (Optional) Strassen's Algorithm.mp4
097 Introduction to Matrix Factorization.mp4
098 Shortcut of LU Decomposition.mp4
099 Real Life LU Decomposition.mp4
100 Why Learning LU Decomposition.mp4
101 2-5 Homework.html
101-Linear-Algebra-2-5-Homework.pdf
102 2-5 Homework Answer.mp4
103 Leontief Closed Model.mp4
104 Leontief Open Model.mp4
105 Computer Graphics.mp4
106 3D Graphics.mp4
107 Subspace.mp4
108 Basis, Column Space, Null Space.mp4
109 2-8 Homework.html
109-Linear-Algebra-2-8-Homework.pdf
110 Error Fix.html
111 2-8 Homework Solution.mp4
112 Coordinate System.mp4
113 Dimension.mp4
114 The Rank Theorem.mp4
115 2-9 Homework.html
115-Linear-Algebra-2-9-Homework.pdf
116 2-9 Homework Solution.mp4

04 - Google Form
117 Google Form.html

05 - Determinants
118 Dot Product.mp4
119 Properties of Dot Product.mp4
120 Schwarz Inequality.mp4
121 Perpendicular and Slope.mp4
122 Cross Product.mp4
123 Plane Equation.mp4
124 Introduction to Determinants.mp4
125 Another Way of Finding Determinant.mp4
126 3-1 Homework.html
126-Linear-Algebra-3-1-Homework.pdf
127 Error Fix.html
128 3-1 Homework Solution.mp4
129 Properties of Determinants.mp4
130 Properties of Determinants II.mp4
131 3-2 Homework.html
131-Linear-Algebra-3-2-Homework.pdf
132 3-2 Homework Solution.mp4
133 Cramer's Law.mp4
134 Cross Product Formula.mp4
135 Parallelepiped Volume.mp4
136 Formula of A Inverse.mp4
137 3-3 Homework.html
137-Linear-Algebra-3-3-Homework.pdf
138 3-3 Homework Solution.mp4
139 Invertible Matrix Theorem.mp4

06 - Vector Space in General
140 Vector Space and Subspace.mp4
141 Subspace.mp4
142 Subspace Spanned by a set of vectors.mp4
143 Theorem of Null Space and Column Space.mp4
144 Linear Transformation, Kernel and Image.mp4
145 4-2 Homework.html
145-Linear-Algebra-4-2-Homework.pdf
146 4-2 Homework Answer.mp4
147 Linearly Independent Set and Basis.mp4
148 4-3 Homework.html
148-Linear-Algebra-4-3-Homework.pdf
149 4-3 Homework Solution.mp4
150 441 The Unique Representation Theorem.mp4
151 B-Coordinate Vector of x.mp4
152 Change of Coordinate Matrix.mp4
153 Linear Independence and Vectors.mp4
154 Isomorphism.mp4
155 4-4 Homework.html
155-Linear-Algebra-4-4-Homework.pdf
156 Quick Fix.html
157 4-4 Homework Solution.mp4
158 Theorem of Linearly Dependence.mp4
159 Dimension General Idea.mp4
160 Dimension of Spaces.mp4
161 4-5 4-6 Homework.html
161-Linear-Algebra-4-5-4-6-Homework.pdf
162 4-5 4-6 Homework Solution.mp4
163 Change of Basis.mp4
164 4-7 Homework.html
164-Linear-Algebra-4-7-Homework.pdf
165 Quick Fix.html
166 4-7 Homework Answer.mp4
167 Notes on 4-8.html
168 Application to Markov Chain.mp4

07 - Eigenvectors and Eigenvalues
169 Eigenvectors and Eigenvalues.mp4
170 Eigenvalues of Triangular Matrix.mp4
171 Analysis of Eigenvalues.mp4
172 Characteristic Equation.mp4
173 Linearly Independent Eigenvectors.mp4
174 Deeper Understanding.mp4
175 5-1 5-2 Homework.html
175-Linear-Algebra-5-1-5-2-Homework.pdf
176 5-1 5-2 Homework Solution.mp4
177 Dynamic System.mp4
178 Similarity and Power of Matrix.mp4
179 Diagonalization Theorem.mp4
180 Diagonalization Examples.mp4
181 5-3 Homework.html
181-Linear-Algebra-5-3-Homework.pdf
182 Homework Solution.mp4
183 Linear Transformation.mp4
184 Linear Transformation from V to V.mp4
185 Linear Transformation in Rn.mp4
186 5-4 Homework.html
186-Linear-Algebra-5-4-Homework.pdf
187 Quick Fix.html
188 5-4 Homework Solution.mp4
189 Complex Eigenvectors and Eigenvalues.mp4
190 Example of Finding Complex Eigenvalues.mp4
191 Complex Conjugate.mp4
192 Rotation Behavior.mp4
193 Rotation and Stretch Matrix.mp4
194 5-5 Homework.html
194-Linear-Algebra-5-5-Homework.pdf
195 5-5 Homework Answer.mp4
196 Discrete Dynamic System.mp4
197 Graphical Description of Solutions.mp4
198 5-7 Note.html
199 Power Method.mp4
200 Example of Power Method.mp4
201 Shifted Inverse Power Method.mp4
202 Gershgorin Circle Theorem.mp4
203 Graphs,Euler Formula.mp4

08 - Inner Product Space
204 Inner Product.mp4
205 Length and Distance.mp4
206 Orthogonality.mp4
207 Projection.mp4
208 6-1 Homework.html
208-Linear-Algebra-6-1-Homework.pdf
209 6-1 Homework Solution.mp4
210 Orthogonal Set.mp4
211 Orthogonal Basis.mp4
212 Orthogonal Projection to Space.mp4
213 Orthonomal Basis.mp4
214 6-2 Homework.html
214-Linear-Algebra-6-2-Homework.pdf
215 6-2 Homework Solution.mp4
216 The Orthogonal Decomposition Theorem.mp4
217 Theorem of Orthonomal Basis.mp4
218 Symbolab with Linear Algebra.html
219 6-3 Homework.html
219-Linear-Algebra-6-3-Homework.pdf
220 Homework Solution.mp4
221 Grand-Schmidt Process.mp4
222 Orthonomal Basis.mp4
223 QR Factorization.mp4
224 6-4 Homework.html
224-Linear-Algebra-6-4-Homework.pdf
225 644 Homework Solution.mp4
226 Inconsistent System.mp4
227 Solution to Least Squares Problem.mp4
228 Example of Least-Squares Solution.mp4
229 Alternative Calculation.mp4
230 Least-Squares Line.mp4
231 Example of Least-Squares Curves.mp4
232 Desmos Line.mp4
233 (Optional) (Calculus) Statistical Regression Line.mp4
234 Inner Product Space.mp4
235 Polynomial Inner Product.mp4
236 Examples.mp4
237 Best Approximation in Inner Product Space.mp4
238 An Inner Product Space for C[a,b].mp4
239 6-7 Homework.html
239-Linear-Algebra-6-7-Homework.pdf
240 6-7 Homework Solution.mp4

09 - End
241 Personal Website.html
242 Survey.html
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