1CHAPTER 1 Introduction to Linear Algebra
24CHAPTER 5 Eigenvalue Problems and Spectral Graph Theory
21.1 Basic Concepts and Definitions
255.1 Eigenvalue Problems and Diagonalization
31.2 Vector Spaces and Subspaces
265.2 Perron-Frobenius Theorem
41.3 Linear Independence and Span
275.3 Spectral Graph Theory
51.4 Linear Transformations
285.4 Applications in Network Analysis
61.5 Eigenvalues and Eigenvectors
29CHAPTER 6
7CHAPTER 2 Systems of Linear Equations
30Optimization and Linear Programming
82.1 Gaussian Elimination
316.1 Introduction to Optimization
92.2 Matrix Algebra
326.2 Linear Programming Problems
102.3 LU Decomposition
336.3 Simplex Method
112.4 QR Decomposition
346.4 Duality in Linear Programming
122.5 Singular Value Decomposition (SVD)
35CHAPTER 7 Applications in Engineering and Physics
13CHAPTER 3 Vector Spaces and Orthogonality
367.1 Control Systems and State-Space Representation
143.1 Inner Product Spaces
377.2 Quantum Mechanics and Dirac Notation
153.2 Orthogonal Projections
387.3 Finite Element Method (FEM)
163.3 Gram-Schmidt Process
397.4 Applications in Signal Processing
173.4 Orthogonal Diagonalization
40CHAPTER 8 Advanced Topics
183.5 Orthogonal Matrices and Least Squares
418.1 Generalized Eigenvectors
19CHAPTER 4 Applications in Data Science
428.2 Jordan Canonical Form
204.1 Principal Component Analysis (PCA)
438.3 Singular Value Decomposition (SVD) Applications
214.2 Singular Value Decomposition (SVD) in Image Compression
448.4 Numerical Linear Algebra Techniques
224.3 Linear Regression and Least Squares Fitting
45Glossaries
234.4 Applications in Machine Learning
46Index
