Basic matrices: An introduction to matrix theory and practice
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Macmillan
1975
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 211 S. |
| ISBN: | 0333186648 0333166922 |
Staff View
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| 100 | 1 | |a Broyden, Charles G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Basic matrices |b An introduction to matrix theory and practice |
| 264 | 1 | |a London |b Macmillan |c 1975 | |
| 300 | |a XII, 211 S. | ||
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| adam_text | Contents
Preface xi
1. Introduction — the Tools of the Trade 1
1.1 Motivation 1
1.2 Sets Involving a Single Subscript — Vectors 3
1.3 Sets Involving Two Subscripts Matrices 6
1.4 Further Consequences and Definitions 12
1.5 Partitioning 14
1.6 Complex Matrices and Vectors 17
Exercises 20
2. Some Elementary Consequences of Linear Independence 25
2.1 Linear Independence 25
2.2 The Unit Matrix 28
2.3 A Fundamental Result 29
2.4 The Inverse Matrix 30
2.5 Particular Nonsingular Matrices 32
2.6 The Solution of Linear Simultaneous Equations 35
2.7 The Sherman—Morrison Formula 37
Exercises 37
3. Matrix and Vector Norms 41
3.1 The Concept of a Norm 41
3.2 Matrix Norms 43
3.3 Explicit Expressions for Matrix Norms 45
3.4 Condition Numbers 47
3.5 Some Further Results 48
3.6 Errors in the Solution of Linear Equations 49
Exercises 51
viii CONTENTS
4. The Practical Solution of Linear Equations 54
4.1 Introduction 54
4.2 LU, or Triangular, Decomposition 56
4.3 Choleski Decomposition 58
4.4 Gaussian Elimination 60
4.5 Numerical Considerations 63
4.6 Iterative Methods 66
4.7 Iterative Improvement 69
Exercises 70
5. Eigenvalues and Eigenvectors 74
5.1 Introduction 74
5.2 Elementary Properties of Eigenvalues 77
5.3 Elementary Properties of Eigenvectors 84
5.4 Eigenvalues and Norms 89
5.5 Convergent Matrices 92
Exercises 95
6. The Practical Evaluation of Eigenvalues and Eigenvectors 99
6.1 Basic Considerations 99
6.2 The Power Method 101
6.3 Inverse Iteration 102
6.4 Jacobi s Method for Real Symmetric Matrices 103
6.5 Elementary Orthogonal Matrices 106
6.6 Reduction to Triangular or Hessenberg Form 109
6.7 Algorithms of QR Type 111
6.8 Numerical Considerations 116
Exercises 121
7. Further Properties of Linear Equations 124
Part 1: General Considerations 124
7.1 The Concept of Rank 124
7.2 The General Set of Linear Equations 128
Part 2: Equations Associated with the Linear Programming Problem 130
7.3 Basic Solutions 130
7.4 Feasible Solutions 135
Exercises 137
8. Scalar Functions of a Vector 139
8.1 The General Scalar Function 139
8.2 Linear and Quadratic Functions 142
CONTENTS ix
8.3 Further Properties of Quadratic Functions 148
8.4 Linear Least squares Problems 154
Exercises 158
9. Linear Programming 160
9.1 The General Linear Programming Problem 160
9.2 The Simplex Method 164
9.3 Calculation of the Initial Feasible Solution 170
9.4 The Resolution of Degeneracy 175
9.5 Computational Variations 179
Exercises 182
10. Duality 186
10.1 The Dual Problem 186
10.2 Complementary Solutions 190
10.3 The Dual Simplex Method 196
Exercises 200
Appendix: Determinants 203
References 207
Index 209
|
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| dewey-tens | 510 - Mathematics |
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| indexdate | 2024-07-09T15:53:20Z |
| institution | BVB |
| isbn | 0333186648 0333166922 |
| language | English |
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| physical | XII, 211 S. |
| publishDate | 1975 |
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| publisher | Macmillan |
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| spelling | Broyden, Charles G. Verfasser aut Basic matrices An introduction to matrix theory and practice London Macmillan 1975 XII, 211 S. txt rdacontent n rdamedia nc rdacarrier Matrices Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Matrizenrechnung (DE-588)4126963-9 s DE-604 Matrix Mathematik (DE-588)4037968-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001932327&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Broyden, Charles G. Basic matrices An introduction to matrix theory and practice Matrices Matrizenrechnung (DE-588)4126963-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4126963-9 (DE-588)4037968-1 (DE-588)4151278-9 |
| title | Basic matrices An introduction to matrix theory and practice |
| title_auth | Basic matrices An introduction to matrix theory and practice |
| title_exact_search | Basic matrices An introduction to matrix theory and practice |
| title_full | Basic matrices An introduction to matrix theory and practice |
| title_fullStr | Basic matrices An introduction to matrix theory and practice |
| title_full_unstemmed | Basic matrices An introduction to matrix theory and practice |
| title_short | Basic matrices |
| title_sort | basic matrices an introduction to matrix theory and practice |
| title_sub | An introduction to matrix theory and practice |
| topic | Matrices Matrizenrechnung (DE-588)4126963-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Matrices Matrizenrechnung Matrix Mathematik Einführung |
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