Linear Algebra. Richard C. Penney

      

      Table of Contents

      1  Cover

      2  LINEAR ALGEBRA

      3  Copyright

      4  PREFACE

      5  FEATURES OF THE TEXT

      6  ACKNOWLEDGMENTS

      7  ABOUT THE COMPANION WEBSITE

      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

      17  ANSWERS AND HINTS

      18  End User License Agreement

      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

.FIGURE 1.2 Vector Algebra.FIGURE 1.3 Example 1.1.FIGURE 1.4 Coordinates in

.FIGURE 1.5 Dependence in

.FIGURE 1.6 Three vectors in

.FIGURE 1.7 Route map.FIGURE 1.8 Dominance in an extended family.FIGURE 1.9 Exercise 1.1.FIGURE 1.10 Exercise 1.43.FIGURE 1.11 Only one solution.FIGURE 1.12 Two planes.FIGURE 1.13 Solution set is a line.