Linear Algebra Using MATLAB

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Table of Contents
Chapter 1Fundament for MATLAB1
1.1MATLAB Desktop1
1.2Vectors and Matrices7
1.3MATLAB Programming11

Chapter 2Introduction to Vectors and Matrices20
2.1Vectors and Linear Combination20
2.2Lengths and Dot s28

Chapter 3Solving Linear Equations40
3.1Vectors and Linear Equations40
3.2The Idea of Elimination45
3.3Elimination Using Matrices52
3.4Inverse Matrices58

Chapter 4Vector Spaces and Subspaces62
4.1Spaces of Vectors62
4.2The Nullspace of matrix64
4.3The Rank and Linear Dependence68

Chapter 5Orthogonality71
5.1 Projections71
5.2Least Squares Approximations75
5.3Orthogonal Bases and Gram-Schmidt Process80

Chapter 6Determinants85
6.1 The Properties of Determinants85
6.2Permutations and Cofactors92
6.3Cramer’s Rule98

Chapter 7Eigenvalues and Eigenvectors102
7.1Introduction to Eigenvalues102
7.2Similar matrices and diagonalization of matrices105
7.3Singular Value Decomposition109

Chapter 8Linear Algebra in Image Processing112
8.1Digital Image Representation112
8.2Geometric Transformation using Matrix Operation114
8.3Image Restoration using Inverse Matrix117
8.4Image Fusion using Principal Component Analysis119
8.5Image Compression using Singular Value Decomposition120

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Linear Algebra Using MATLAB