Linear Algebra. Richard C. Penney

      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

      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

      1 Chapter 1FIGURE 1.1 Coordinates in

FIGURE 1.4 Coordinates in

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FIGURE 1.5 Dependence in

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FIGURE 1.6 Three vectors in

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