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Vector Spaces
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Prerequisites
Algebraic Structures
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1 Sets
1.1 Sets
1.2 Cardinality
1.3 Some Commonly Used Sets
1.4 Subset and Superset
1.5 Equal Sets
1.6 Complement
1.7 Union
1.8 Intersection
1.9 Collection of Sets
1.10 Partitioning of Set
1.11 Cartesian Product of n Copies of a Set
1.12 Truth
1.13 List
2 Functions
2.1 Introduction
2.2 Remarks
2.3 Domain, Codomain and Range
2.4 Image and Preimage
2.5 Ill-Defined Functions
2.6 Exercise
2.7 Injection, Surjection and Bijection
2.8 Identity Function
2.9 Equal Functions
2.10 Exercise
2.11 Composition
2.12 Associativity
2.13 Exercise
2.14 Left Inverse
2.15 Exercise
2.16 Exercise
2.17 Exercise
2.18 Exercise
2.19 Right Inverse
2.20 Exercise
2.21 Exercise
2.22 Exercise
2.23 Exercise
3 Fields
3.1 Field Axioms
3.2 Remarks
3.3 Truths
3.4 Exercise
3.5 Exercise
3.6 Exercise
3.7 Exercise
3.8 Exercise
3.9 Exercise
3.10 Field Examples
3.11 Exercise
3.12 Exercise
4 Vector Spaces
4.1 Introduction
4.2 Axioms
4.3 Remarks
4.4 Truths
4.5 Exercise
4.6 Exercise
4.7 Exercise
4.8 Exercise
4.9 Truths
4.10 Exercise
4.11 Exercise
4.12 Exercise
5 Subspaces
5.1 Sum of Subsets
5.2 Truths
5.3 Exercise
6 Linear Combination of Vectors
6.1 Introduction
6.2 Truth
Course Information
Teacher
Teacher: Simerdeep Singh
Cosmic Notes
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Memory-Aid
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Email: mycosmicschool@gmail.com
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