Elementary Linear Algebra
Pearson Education Limited (Verlag)
978-1-292-02503-2 (ISBN)
PREFACE ix
TO THE STUDENT xv
CHAPTER 1 MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS 1
1.1 Matrices and Vectors 1
1.2 Linear Combinations, Matrix—Vector Products, and Special Matrices 11
1.3 Systems of Linear Equations 25
1.4 Gaussian Elimination 39
1.5* Applications of Systems of Linear Equations 54
1.6 The Span of a Set of Vectors 64
1.7 Linear Dependence and Linear Independence 73
Chapter 1 Review Exercises
Chapter 1 MATLAB Exercises
CHAPTER 2 MATRICES AND LINEAR TRANSFORMATIONS 90
2.1 Matrix Multiplication 90
2.2* Applications of Matrix Multiplication 101
2.3 Invertibility and Elementary Matrices 117
2.4 The Inverse of a Matrix 130
2.5* Partitioned Matrices and Block Multiplication 141
2.6* The LU Decomposition of a Matrix 147
2.7 Linear Transformations and Matrices 162
2.8 Composition and Invertibility of Linear Transformations 175
Chapter 2 Review Exercises
Chapter 2 MATLAB Exercises
CHAPTER 3 DETERMINANTS 192
3.1 Cofactor Expansion 192
3.2 Properties of Determinants 204
Chapter 3 Review Exercises
Chapter 3 MATLAB Exercises
CHAPTER 4 SUBSPACES AND THEIR PROPERTIES 218
4.1 Subspaces 218
4.2 Basis and Dimension 232
4.3 The Dimension of Subspaces Associated with a Matrix 245
4.4 Coordinate Systems 254
4.5 Matrix Representations of Linear Operators 266
Chapter 4 Review Exercises
Chapter 4 MATLAB Exercises
CHAPTER 5 EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION 282
5.1 Eigenvalues and Eigenvectors 282
5.2 The Characteristic Polynomial 291
5.3 Diagonalization of Matrices 302
5.4* Diagonalization of Linear Operators 314
5.5* Applications of Eigenvalues 323
Chapter 5 Review Exercises
Chapter 5 MATLAB Exercises
CHAPTER 6 VECTOR SPACES 473
6.1 Vector Spaces and Their Subspaces 473
6.2 Linear Transformations 485
6.3 Basis and Dimension 495
6.4 Matrix Representations of Linear Operators 505
6 .5 Inner Product Spaces 517
Chapter 6 Review Exercises
Chapter 6 MATLAB Exercises
CHAPTER 7 ORTHOGONALITY 347
7.1 The Geometry of Vectors 347
7.2 Orthogonal Vectors 360
7.3 Orthogonal Projections 374
7.4 Least-Squares Approximations and Orthogonal Projections 388
7.5 Orthogonal Matrices and Operators 398
7.6 Symmetric Matrices 412
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| Verlagsort | Harlow |
|---|---|
| Sprache | englisch |
| Maße | 218 x 275 mm |
| Gewicht | 1200 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-292-02503-4 / 1292025034 |
| ISBN-13 | 978-1-292-02503-2 / 9781292025032 |
| Zustand | Neuware |
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