Читать книгу Linear Algebra - Richard C. Penney - Страница 2

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