Matrix methods: applied linear algebra
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier [u.a.]
2009
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | XV, 416 S. graph. Darst. |
| ISBN: | 9780123744272 |
Internformat
MARC
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| 100 | 1 | |a Bronson, Richard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Matrix methods |b applied linear algebra |c Richard Bronson ; Gabriel B. Costa |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier [u.a.] |c 2009 | |
| 300 | |a XV, 416 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | |a Costa, Gabriel B. |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804139093118943232 |
|---|---|
| adam_text | Titel: Matrix methods
Autor: Bronson, Richard
Jahr: 2009
Contents
Preface xi
About the Authors xiii
Acknowledgments xv
1 Matrices 1
1.1 Basic Concepts 1
Problems 1.1 3
1.2 Operations 6
Problems 1.2 8
1.3 Matrix Multiplication 9
Problems 1.3 16
1.4 Special Matrices 19
Problems 1.4 23
1.5 Submatrices and Partitioning
Problems 1.5 32
1.6 Vectors 33
Problems 1.6 34
1.7 The Geometry of Vectors 37
Problems 1.7 41
29
2 Simultaneous Linear Equations 43
2.1 Linear Systems 43
Problems 2.1 45
2.2 Solutions by Substitution
Problems 2.2 54
2.3 Gaussian Elimination 54
Problems 2.3 62
50
vii
viii Contents
2.4 Pivoting Strategies 65
Problems 2.4 70
2.5 Linear Independence 71
Problems 2.5 76
2.6 Rank 78
Problems 2.6 83
2.7 Theory of Solutions 84
Problems 2.7 87
2.8 Final Comments on Chapter 2 88
3 The Inverse 93
3.1 Introduction 93
Problems 3.1 98
3.2 Calculating Inverses 101
Problems 3.2 106
3.3 Simultaneous Equations 109
Problems 3.3 111
3.4 Properties of the Inverse 112
Problems 3.4 114
3.5 LU Decomposition 115
Problems 3.5 121
3.6 Final Comments on Chapter 3 124
4 An Introduction to Optimization 127
4.1 Graphing Inequalities 127
Problems 4.1 130
4.2 Modeling with Inequalities 131
Problems 4.2 133
4.3 Solving Problems Using Linear Programming 135
Problems 4.3 140
4.4 An Introduction to The Simplex Method 140
Problems 4.4 147
4.5 Final Comments on Chapter 4 147
5 Determinants 149
5.1 Introduction 149
Problems 5.1 150
5.2 Expansion by Cofactors 152
Problems 5.2 155
5.3 Properties of Determinants 157
Problems 5.3 161
5.4 Pivotal Condensation 163
Problems 5.4 166
Contents ix
5.5 Inversion 167
Problems 5.5 169
5.6 Cramer s Rule 170
Problems 5.6 173
5.7 Final Comments on Chapter 5 173
6 Eigenvalues and Eigenvectors 177
6.1 Definitions 177
Problems 6.1 179
6.2 Eigenvalues 180
Problems 6.2 183
6.3 Eigenvectors 184
Problems 6.3 188
6.4 Properties of Eigenvalues and Eigenvectors 190
Problems 6.4 193
6.5 Linearly Independent Eigenvectors 194
Problems 6.5 200
6.6 Power Methods 201
Problems 6.6 211
7 Matrix Calculus 213
7.1 Weil-Defined Functions 213
Problems 7.1 216
7.2 Cayley-Hamilton Theorem 219
Problems 7.2 221
7.3 Polynomials of Matrices-Distinct Eigenvalues 222
Problems 7.3 226
7.4 Polynomials of Matrices?General Case 228
Problems 7.4 232
7.5 Functions of a Matrix 233
Problems 7.5 236
7.6 The Function eAf 238
Problems 7.6 240
7.7 Complex Eigenvalues 241
Problems 7.7 244
7.8 Properties of eA 245
Problems 7.8 247
7.9 Derivatives of a Matrix 248
Problems 7.9 253
7.10 Final Comments on Chapter 7 254
Contents
8 Linear Differential Equations 257
8.1 Fundamental Form 257
Problems 8.1 261
8.2 Reduction of an nth Order Equation 263
Problems 8.2 269
8.3 Reduction of a System 269
Problems 8.3 274
8.4 Solutions of Systems with Constant Coefficients 275
Problems 8.4 285
8.5 Solutions of Systems?General Case 286
Problems 8.5 294
8.6 Final Comments on Chapter 8 295
9 Probability and Markov Chains 297
9.1 Probability: An Informal Approach 297
Problems 9.1 300
9.2 Some Laws of Probability 301
Problems 9.2 304
9.3 Bernoulli Trials and Combinatorics 305
Problems 9.3 309
9.4 Modeling with Markov Chains: An Introduction 310
Problems 9.4 313
9.5 Final Comments on Chapter 9 314
10 Real Inner Products and Least-Square 315
10.1 Introduction 315
Problems 10.1 317
10.2 Orthonormal Vectors 320
Problems 10.2 325
10.3 Projections and QR-Decompositions 327
Problems 10.3 337
10.4 The QR-Algorithm 339
Problems 10.4 343
10.5 Least-Squares 344
Problems 10.5 352
Appendix: A Word on Technology 355
Answers and Hints to Selected Problems 357
Index 411
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:38:36Z |
| institution | BVB |
| isbn | 9780123744272 |
| language | English |
| lccn | 2008277872 |
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| spelling | Bronson, Richard Verfasser aut Matrix methods applied linear algebra Richard Bronson ; Gabriel B. Costa 3. ed. Amsterdam [u.a.] Elsevier [u.a.] 2009 XV, 416 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Matrices Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s DE-604 Costa, Gabriel B. Sonstige oth http://www.loc.gov/catdir/enhancements/fy0902/2008277872-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017538486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bronson, Richard Matrix methods applied linear algebra Matrices Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4037968-1 |
| title | Matrix methods applied linear algebra |
| title_auth | Matrix methods applied linear algebra |
| title_exact_search | Matrix methods applied linear algebra |
| title_full | Matrix methods applied linear algebra Richard Bronson ; Gabriel B. Costa |
| title_fullStr | Matrix methods applied linear algebra Richard Bronson ; Gabriel B. Costa |
| title_full_unstemmed | Matrix methods applied linear algebra Richard Bronson ; Gabriel B. Costa |
| title_short | Matrix methods |
| title_sort | matrix methods applied linear algebra |
| title_sub | applied linear algebra |
| topic | Matrices Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Matrices Matrix Mathematik |
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