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CHAPTER 4 General Vector Spaces
- 4.1 Vector Space 08:43
- 4.1 Examples of Vector Space 10:44
- 4.1 More Examples of Vector Space 07:58
- 4.1 The Vector Space of Real Valued Function 09:49
- 4.1 A Set that is Not a Vector Space 04:30
- 4.1 An Unusual Vector Space 12:12
- 4.1 Exercise 11 11:02
- 4.1 Extra Example of a Set that is Not a Vector Space 08:38
- 4.2 The Meaning of subspace 07:25
- 4.2 Subspaces of R2 10:10
- 4.2 Subspaces of R3 and Mnn 09:26
- 4.2 Subspaces of Funations 09:12
- 4.2 Linear Combination 06:31
- 4.2 Example ( Is w a linear combination of Other Vectors ? ) 11:57
- 4.2 Spanning Set 11:55
- 4.2 Testing for Spanning 12:19
- 4.2 Equal Spanning Sets 04:26
- 4.2 The Solution of a Homogeneous linear System 04:05
- 4.2 Solution Spaces of Homogeneous Linear System 07:20
- 4.2 Matrix Transformation 03:35
- 4.3 Linearly independence 22:18
- 4.3 Linearly Independent of Polynomials 13:32
- 4.3 Wronskian 14:49
- 4.4 Basis 13:27
- 4.4 Uniqueness of Basis Representation 06:51
- 4.4 Coordinates 09:29
- 4.5 Dimension 09:53
- 4.5 Plus Minus Theorem 26:05
- 4.6 Change of Basis (Basic Idea) 18:34
- 4.6 Finding Transition Matrix and Computing coordinates vectors (Example 1 and 2) 18:52
- 4.6 Invertibility of Transition Matrix - Learning New Procedure to Compute Transition Matrix 10:52
- 4.7 Row Space, Vector Space, Null Space 07:56
- 4.7 The Relationship Between Ax=b and col(A) and null(A) 16:03
- 4.7 Basis of null(A) 08:46
- 4.7 Basis for row(A) and Col(A) 10:38
- 4.7 Basis for the Space Spanned by a Set of Vectors 14:53
- 4.7 summarize 05:14
- 4.8 Rank and nullity 08:52
- 4.8 Some Theorems about Rank and nullity 11:30
- 4.8 The fundamental spaces of a Matrix 07:19
- 1.8 Matrix Transformation 12:46
- 1.8 Standard Matrix 15:21
- 4.8 Overdetermind and underdetermind 12:32
- 4.9 Reflection Operator 13:28
- 4.9 Projection Operator 15:50
- 4.9 Dilation and Contraction 08:34
- 4.10 Composition of Matrix Transformation 09:13
- 4.10 Examples of Composition 19:41
- 4.10 One-to-one Matrix Transformation 07:03
- 4.10 Kernel and Range 10:40
- 4.10 Inverse Operator 09:59
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CHAPTER 4 General Vector Spaces
