Applied linear algebra:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ
Prentice-Hall
1988
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 521 S. graph. Darst. |
| ISBN: | 0130412600 |
Staff View
MARC
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| 245 | 1 | 0 | |a Applied linear algebra |c Ben Noble and James W. Daniel |
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Record in the Search Index
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| adam_text | Contents
PREFACE xi
ON THE USE OF COMPUTERS xv
Chapter 1: MATRIX ALGEBRA 1
1.1 Introduction 1
1.2 Equality, addition, and multiplication by a scalar 3
1.3 Matrix multiplication 8
1.4 Matrix inverses 21
1.5 Partitioned matrices 33
1.6 Miscellaneous problems 40
Chapter 2: SOME SIMPLE APPLICATIONS AND QUESTIONS 42
2.1 Introduction 42
2.2 Business competition: Markov chains 43
2.3 Population growth: powers of a matrix 50
2.4 Equilibrium in networks: linear equations 54
2.5 Oscillatory systems: eigenvalues 60
2.6 General modeling: least squares 66
2.7 Production planning: linear programs 73
2.8 Miscellaneous problems 79
Chapter 3: SOLVING EQUATIONS AND FINDING INVERSES: METHODS 82
3.1 Introduction 82
3.2 Solving equations by Gauss elimination 83
viii Contents
3.3 Existence of solutions to systems of equations: some examples and
procedures 95
3.4 Finding inverses by Gauss elimination 100
3.5 Row operations and elementary matrices 103
3.6 Choosing pivots for Gauss elimination in practice 707
3.7 The L {/ decomposition 116
3.8 Work measures and solving slightly modified systems 125
3.9 Computer software for Gauss elimination 134
3.10 Miscellaneous problems 136
Chapter* SOLVING EQUATIONS AND FINDING INVERSES: THEORY 139
4.1 Introduction 139
4.2 Gauss reduced form and rank 140
4.3 Solvability and solution sets for systems of equations 147
AA Inverses and rank 755
4.5 Determinants and their properties 158
4.6 Determinantal representation of inverses and solutions 167
4.7 Miscellaneous problems 772
Chapter 5: VECTORS AND VECTOR SPACES 175
5.1 Introduction; geometrical vectors 775
5.2 General vector spaces 181
5.3 Linear dependence and linear independence 187
5.4 Basis, dimension, and coordinates 195
5.5 Bases and matrices 207
5.6 Length and distance in vector spaces: norms 275
5.7 Angle in vector spaces: inner products 220
5.8 Orthogonal projections and bases: general spaces and Gram Schmidt 226
5.9 Orthogonal projections and bases: W, C, QR, and least squares 234
5.10 Miscellaneous problems 246
Chapter 6: LINEAR TRANSFORMATIONS AND MATRICES 249
6.1 Introduction; linear transformations 249
6.2 Matrix representations of linear transformations 257
6.3 Norms of linear transformations and matrices 263
6.4 Inverses of perturbed matrices; condition of linear equations 268
6.5 Miscellaneous problems 277
Contents ix
Chapter 7: EIGENVALUES AND EIGENVECTORS: AN OVERVIEW 279
7.1 Introduction 279
7.2 Definitions and basic properties 284
7.3 Eigensystems, decompositions, and transformation representations 293
7.4 Similarity transformations; Jordan form 299
7.5 Unitary matrices and unitary similarity; Schur and diagonal forms 304
7.6 Computer software for rinding eigensystems 575
7.7 Condition of eigensystems 317
7.8 Miscellaneous problems 322
Chapter 8: EIGENSYSTEMS OF SYMMETRIC, HERMITIAN, AND
NORMAL MATRICES, WITH APPLICATIONS 325
8.1 Introduction 325
8.2 Schur form and decomposition; normal matrices 326
8.3 Eigensystems of normal matrices 331
8.4 Application: singular value decomposition 338
8.5 Application: least squares and the pseudoinverse 346
8.6 Miscellaneous problems 353
Chapter 9: EIGENSYSTEMS OF GENERAL MATRICES, WITH APPLICATIONS 355
9.1 Introduction 555
9.2 Jordan form 357
9.3 Eigensystems for general matrices 364
9.4 Application: discrete system evolution and matrix powers 369
9.5 Application: continuous system evolution and matrix exponentials 378
9.6 Application: iterative solution of linear equations 388
9.7 Miscellaneous problems 395
Chapter 10: QUADRATIC FORMS AND VARIATIONAL CHARACTERIZATIONS
OF EIGENVALUES 398
10.1 Introduction 398
10.2 Quadratic forms in U2 400
10.3 Quadratic forms in W and C 407
10.4 Extremizing quadratic forms: Rayleigh s principle 415
10.5 Extremizing quadratic forms: the min max principle 423
10.6 Miscellaneous problems 428
x Contents
Chapter 11: LINEAR PROGRAMMING 433
11.1 Analysis of a simple example 433
11.2 A general linear program 448
11.3 Solving a general linear program 454
11.4 Duality 465
11.5 Miscellaneous problems 475
Appendix 1: ANSWERS AND AIDS TO SELECTED PROBLEMS 479
Appendix 2: BIBLIOGRAPHY 502
INDEX OF NOTATION 505
SUBJECT INDEX 509
|
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| dewey-sort | 3512 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:08:45Z |
| institution | BVB |
| isbn | 0130412600 |
| language | English |
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| physical | XVI, 521 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
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| spelling | Noble, Ben Verfasser aut Applied linear algebra Ben Noble and James W. Daniel 3. ed. Englewood Cliffs, NJ Prentice-Hall 1988 XVI, 521 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algèbre linéaire Álgebra linear (aplicações) larpcal Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 Daniel, James W. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002573862&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Noble, Ben Daniel, James W. Applied linear algebra Algèbre linéaire Álgebra linear (aplicações) larpcal Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Applied linear algebra |
| title_auth | Applied linear algebra |
| title_exact_search | Applied linear algebra |
| title_full | Applied linear algebra Ben Noble and James W. Daniel |
| title_fullStr | Applied linear algebra Ben Noble and James W. Daniel |
| title_full_unstemmed | Applied linear algebra Ben Noble and James W. Daniel |
| title_short | Applied linear algebra |
| title_sort | applied linear algebra |
| topic | Algèbre linéaire Álgebra linear (aplicações) larpcal Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Álgebra linear (aplicações) Algebras, Linear Lineare Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002573862&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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