Lecture 02 Linear Algebra Basics
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- Erika Floyd
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1 Introduction to Computational Data Analysis CX4240, 2019 Spring Lecture 02 Linear Algebra Basics Chao Zhang College of Computing Georgia Tech These slides are based on slides from Le Song and Andres Mendez-Vazquez.
2 Outline Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Singular Value Decomposition Matrix Calculus 2
3 Why Linear Algebra?
4 Linear Algebra Basics 4
5 Outline Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Singular Value Decomposition Matrix Calculus 5
6 Norms 6
7 Norms 7
8 Vector Norm Examples 8
9 Special Matrices 9
10 Outline Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Singular Value Decomposition Matrix Calculus 10
11 Multiplications 11
12 Multiplications 12
13 Inner Product Properties 13
14 Inner Product Properties 14
15 Inner Product Properties 15
16 Outline Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Matrix Decomposition Matrix Calculus 16
17 Linear Independence and Matrix Rank 17
18 Range and Null Space 18
19 Row and Column Space 19
20 Matrix Rank: Examples What are the ranks for the following matrices? 20
21 Matrix Inverse 21
22 Outline Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Singular Value Decomposition Matrix Calculus 22
23 Matrix Trace 23
24 Matrix Determinant 24
25 Properties of Matrix Determinant 25
26 Outline Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Singular Value Decomposition Matrix Calculus 26
27 Eigenvalues and Eigenvectors 27
28 Computing Eigenvalues and Eigenvectors 28
29 Eigenvalue Example Slide credit: Shubham Kumbhar 29
30 Matrix Eigen Decomposition 30
31 Properties of Eigendecomposition 31
32 Outline Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Singular Value Decomposition Matrix Calculus 32
33 Singular Value Decomposition 33
34 Singular Value Decomposition 34
35 Geometric Meaning of SVD Image Credit: Kevin Binz 35
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37 Outline Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Singular Value Decomposition Matrix Calculus 37
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39 Summary Linear Algebra Basics Norms Multiplications Matrix Inversion Trace and Determinant Eigen Values and Eigen Vectors Singular Value Decomposition Matrix Calculus 39
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