Table of Contents
1 Cover
4 PREFACE
8 CHAPTER 1: SYSTEMS OF LINEAR EQUATIONS 1.1 THE VECTOR SPACE OF m × n MATRICES 1.2 SYSTEMS 1.3 GAUSSIAN ELIMINATION 1.4 COLUMN SPACE AND NULLSPACE Notes
9 CHAPTER 2: LINEAR INDEPENDENCE AND DIMENSION2.1 THE TEST FOR LINEAR INDEPENDENCE2.2 DIMENSION2.3 ROW SPACE AND THE RANK‐NULLITY THEOREMNotes
10 CHAPTER 3: LINEAR TRANSFORMATIONS3.1 THE LINEARITY PROPERTIES3.2 MATRIX MULTIPLICATION (COMPOSITION)3.3 INVERSES3.4 The LU Factorization3.5 THE MATRIX OF A LINEAR TRANSFORMATIONNote
11 CHAPTER 4: DETERMINANTS 4.1 DEFINITION OF THE DETERMINANT 4.2 REDUCTION AND DETERMINANTS 4.3 A FORMULA FOR INVERSES
12 CHAPTER 5: EIGENVECTORS AND EIGENVALUES 5.1 EIGENVECTORS 5.2 DIAGONALIZATION 5.3 COMPLEX EIGENVECTORS
13 CHAPTER 6: ORTHOGONALITY6.1 THE SCALAR PRODUCT IN6.2 PROJECTIONS: THE GRAM–SCHMIDT PROCESS6.3 FOURIER SERIES: SCALAR PRODUCT SPACES6.4 ORTHOGONAL MATRICES6.5 LEAST SQUARES6.6 QUADRATIC FORMS: ORTHOGONAL DIAGONALIZATION6.7 THE SINGULAR VALUE DECOMPOSITION (SVD)6.8 HERMITIAN SYMMETRIC AND UNITARY MATRICESNote
14 CHAPTER 7: GENERALIZED EIGENVECTORS7.1 GENERALIZED EIGENVECTORSEXERCISES7.2 CHAIN BASESNote
15 CHAPTER 8: NUMERICAL TECHNIQUES 8.1 CONDITION NUMBER 8.2 COMPUTING EIGENVALUES Notes
16 Index
List of Tables
1 Chapter 1TABLE 1.1 Profits: 2019
2 Chapter 3TABLE 3.1 Demand TableTABLE 3.2 Annual Fees: 2020–2025 (in thousands)
3 Chapter 5TABLE 5.1Gauss Auto Rental
List of Illustrations
1 Chapter 1FIGURE 1.1 Coordinates in 
