Verfügbarkeit: Applied linear algebra | Technische Universität München

Applied linear algebra:

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Bibliographische Detailangaben
Beteiligte Personen:	Noble, Ben (VerfasserIn), Daniel, James W. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Englewood Cliffs, NJ Prentice-Hall 1988
Ausgabe:	3. ed.
Schlagwörter:	Algèbre linéaire Álgebra linear (aplicações) Algebras, Linear Lineare Algebra
Links:	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
Umfang:	XVI, 521 S. graph. Darst.
ISBN:	0130412600

Internformat

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Datensatz im Suchindex

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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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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
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