Linear algebra and its applications: 1 A first course
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Chichester u.a.
Horwood u.a.
1989
|
| Ausgabe: | 1. publ |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 289 S. Ill. |
| ISBN: | 0853129460 074580571X 047021242X |
Internformat
MARC
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| 100 | 1 | |a Griffel, David H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear algebra and its applications |n 1 |p A first course |c D. H. Griffel |
| 250 | |a 1. publ | ||
| 264 | 1 | |a Chichester u.a. |b Horwood u.a. |c 1989 | |
| 300 | |a XIII, 289 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Table of Contents
Contents of Volume 2 viii
Preface xi
PART I VECTORS AND MATRICES
Chapter 1 Elementary Vector Algebra
1A Introduction to Vectors 3
IB Elementary Vector Algebra 6
1C Two Dimensional Vectors: Basis and Components 11
ID Three Dimensional Vectors 15
IE The dot product 17
IF n Vectors 22
Problems 24
Chapter 2 Matrices
2A Basic Ideas 27
2B Matrix Algebra 30
2C Matrix Multiplication 32
2D The Algebra of Matrix Multiplication 37
2E Inverses 41
2F Partitioned Matrices 44
Problems 47
PART II VECTOR SPACES AND LINEAR EQUATIONS
Chapter 3 Vector Spaces
3A Introduction 55
3B Vector Spaces 56
3C Algebraic Properties of Vector Spaces 60
3D Subspaces 62
3E Spanning Sets 65
3F Linear Dependence 67
3G Basis and Dimension 70
3H The Dimension of a Subspace 72
31 Components 74
3J* Isomorphism of Vector Spaces 76
3K* Sums and Complements of Subspaces 79
3L* The Theory of Colour Vision 83
3M Proofs of Theorems on Dimension 87
Problems 89
Chapter 4 Elementary Operations and Linear Equations
4A Vectors in Echelon Form 95
4B Elementary Operations 97
4C Sets of Linear Equations 100
4D Gaussian Elimination 103
4E Further Aspects of Gaussian Elimination 107
4F Rank 108
4G Gauss Jordan Elimination Ill
4H The Rank Theorem 114
41 Matrix Inverses 116
4J* Practical Aspects of Gaussian Elimination 118
4K* Iterative Methods for Linear Equations 121
4L* Elementary Matrices 125
4M* Triangular Factorisation 127
4N Proofs 131
Problems 133
PART HI LINEAR TRANSFORMATIONS
Chapter 5 Linear Transformations on Vector Spaces
5A Basic Definitions 141
5B The Image and Rank of a Linear Transformation 144
5C The Null Space of a Linear Transformation 148
5D Linear Equations 151
5E Inverses 154
5F Eigenvectors 156
5G* Eigenvalues and Vibrating Systems 159
5H Eigenvalue Problems 163
51* Rotations and Orthogonal Matrices 167
5J* The Power Method 170
5K* The Algebra of Linear Transformations 174
5L Proofs of Theorems 177
Problems 181
Chapter 6 Determinants
6A Transformations of the Plane 189
6B n by n Determinants 192
6C Other Ways of Evaluating Determinants 196
6D* The Permutation Definition of Determinants 200
6E* The Multiplication Theorem 205
6F* The Adjugate Matrix 206
Problems 207
Chapter 7 Eigenvalue Problems and the Characteristic Equation
7A The Characteristic Equation 211
7B Multiple Eigenvalues 215
7C* Gershgorin s Theorem 216
7D* The Spectral Radius and its Applications 219
7E Proofs of Theorems 223
Problems 224
Chapter 8 Diagonalisation of Matrices and Quadratic Forms
8A Diagonal Factorisation 228
8B* Application of Diagonalisation to Differential Equations 231
8C Symmetric Matrices and Orthogonal Diagonalisation 234
8D Quadratic Forms in Two Variables 237
8E Quadratic Forms in n Variables 239
8F Conic Sections and Quadric Surfaces 241
Problems 245
Appendices
A How to Read Mathematics 250
B Mathematical Induction 253
C Sets 254
D Functions 256
E Complex Numbers 259
F Polynomials 262
G Fields. 265
H Historical Notes 268
Solutions to Exercises 271
Hints and Answers to Selected Problems 277
References and Bibliography 285
Index 287
|
| adam_txt |
Table of Contents
Contents of Volume 2 viii
Preface xi
PART I VECTORS AND MATRICES
Chapter 1 Elementary Vector Algebra
1A Introduction to Vectors 3
IB Elementary Vector Algebra 6
1C Two Dimensional Vectors: Basis and Components 11
ID Three Dimensional Vectors 15
IE The dot product 17
IF n Vectors 22
Problems 24
Chapter 2 Matrices
2A Basic Ideas 27
2B Matrix Algebra 30
2C Matrix Multiplication 32
2D The Algebra of Matrix Multiplication 37
2E Inverses 41
2F Partitioned Matrices 44
Problems 47
PART II VECTOR SPACES AND LINEAR EQUATIONS
Chapter 3 Vector Spaces
3A Introduction 55
3B Vector Spaces 56
3C Algebraic Properties of Vector Spaces 60
3D Subspaces 62
3E Spanning Sets 65
3F Linear Dependence 67
3G Basis and Dimension 70
3H The Dimension of a Subspace 72
31 Components 74
3J* Isomorphism of Vector Spaces 76
3K* Sums and Complements of Subspaces 79
3L* The Theory of Colour Vision 83
3M Proofs of Theorems on Dimension 87
Problems 89
Chapter 4 Elementary Operations and Linear Equations
4A Vectors in Echelon Form 95
4B Elementary Operations 97
4C Sets of Linear Equations 100
4D Gaussian Elimination 103
4E Further Aspects of Gaussian Elimination 107
4F Rank 108
4G Gauss Jordan Elimination Ill
4H The Rank Theorem 114
41 Matrix Inverses 116
4J* Practical Aspects of Gaussian Elimination 118
4K* Iterative Methods for Linear Equations 121
4L* Elementary Matrices 125
4M* Triangular Factorisation 127
4N Proofs 131
Problems 133
PART HI LINEAR TRANSFORMATIONS
Chapter 5 Linear Transformations on Vector Spaces
5A Basic Definitions 141
5B The Image and Rank of a Linear Transformation 144
5C The Null Space of a Linear Transformation 148
5D Linear Equations 151
5E Inverses 154
5F Eigenvectors 156
5G* Eigenvalues and Vibrating Systems 159
5H Eigenvalue Problems 163
51* Rotations and Orthogonal Matrices 167
5J* The Power Method 170
5K* The Algebra of Linear Transformations 174
5L Proofs of Theorems 177
Problems 181
Chapter 6 Determinants
6A Transformations of the Plane 189
6B n by n Determinants 192
6C Other Ways of Evaluating Determinants 196
6D* The Permutation Definition of Determinants 200
6E* The Multiplication Theorem 205
6F* The Adjugate Matrix 206
Problems 207
Chapter 7 Eigenvalue Problems and the Characteristic Equation
7A The Characteristic Equation 211
7B Multiple Eigenvalues 215
7C* Gershgorin's Theorem 216
7D* The Spectral Radius and its Applications 219
7E Proofs of Theorems 223
Problems 224
Chapter 8 Diagonalisation of Matrices and Quadratic Forms
8A Diagonal Factorisation 228
8B* Application of Diagonalisation to Differential Equations 231
8C Symmetric Matrices and Orthogonal Diagonalisation 234
8D Quadratic Forms in Two Variables 237
8E Quadratic Forms in n Variables 239
8F Conic Sections and Quadric Surfaces 241
Problems 245
Appendices
A How to Read Mathematics 250
B Mathematical Induction 253
C Sets 254
D Functions 256
E Complex Numbers 259
F Polynomials 262
G Fields. 265
H Historical Notes 268
Solutions to Exercises 271
Hints and Answers to Selected Problems 277
References and Bibliography 285
Index 287 |
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| spelling | Griffel, David H. Verfasser aut Linear algebra and its applications 1 A first course D. H. Griffel 1. publ Chichester u.a. Horwood u.a. 1989 XIII, 289 S. Ill. txt rdacontent n rdamedia nc rdacarrier (DE-604)BV002304317 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015357091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Griffel, David H. Linear algebra and its applications |
| title | Linear algebra and its applications |
| title_auth | Linear algebra and its applications |
| title_exact_search | Linear algebra and its applications |
| title_exact_search_txtP | Linear algebra and its applications |
| title_full | Linear algebra and its applications 1 A first course D. H. Griffel |
| title_fullStr | Linear algebra and its applications 1 A first course D. H. Griffel |
| title_full_unstemmed | Linear algebra and its applications 1 A first course D. H. Griffel |
| title_short | Linear algebra and its applications |
| title_sort | linear algebra and its applications a first course |
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