Introduction to linear algebra:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. u.a.
Addison-Wesley
1989
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 578 S. |
| ISBN: | 0201168332 |
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MARC
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| 245 | 1 | 0 | |a Introduction to linear algebra |c Lee W. Johnson ; R. Dean Riess ; Jimmy T. Arnold |
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Record in the Search Index
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I!
i
SECONDEDITION
Introduction to
Linear Algebra
LEE W JOHNSON
R DEAN RIESS
JIMMY T ARNOLD
Virginia Polytechnic Institute and State University
Addison-Wesley Reading Massachusetts * Menlo Park, California • New York
Publishing Company j Don Mills, Ontario • Wokingham, England • Amsterdam • Bonn
! Sydney • Singapore • Tokyo • Madrid • San Juan
£ ••
Contents
1 Matrices and Systems of Linear Equations 1
1 Introduction and Gaussian Elimination 1
2 Solution Sets for Linear Systems 11
3 Matrices and Echelon Form 22
4 Consistent Systems of Linear Equations 36
5 Matrix Operations 44
6 Algebraic Properties of Matrix Operations 58
7 Linear Independence and Nonsingular Matrices 66
8 Data Fitting Numerical Integration, and Numerical
Differentiation (Optional) 76
9 Matrix Inverses and Their Properties 88
10 Finding the Inverse of a Nonsingular Matrix 97
The Vector Space R 109
2 1 Introduction 109
2 2 Vector Space Properties of R 113
2 3 Examples of Subspaces 121
2 4 Bases for Subspaces 135
2 5 Dimension 148
2 6 Orthogonal Bases for Subspaces 161
ix
Contents
2 7 Linear Transformations from R to Rm 172
2 8 The Least-Squares Problem in Rn (Optional)
2 9 Fitting Data and Least-Squares Solutions of
Overdetermined Systems (Optional) 200
The Eigenvalue Problem 211
3 1 Introduction 211
3 2 Determinants and the Eigenvalue Problem 215
3 3 Elementary Operations and Determinants (Optional) 224
3 4 Eigenvalues and the Characteristic Polynomial 233
3 5 Eigenvectors and Eigehspaces 243
3 6 Complex Eigenvalues and Eigenvectors 252
3 7 Similarity Transformations and Diagonalization 261
3 8 Applications (Optional) 274
Vector Spaces and Linear Transformations 287
4 1 Introduction 287
4 2 Vector Spaces 288
4 3 Subspaces 297
4 4 Linear Independence Bases, and Coordinates 305
4 5 Dimension 318 •
4 6 lnner:Product Spaces Orthogonal Bases, and
Projections (Optional) 324
4 7 Linear Transformations 334
4 8 Operations with Linear Transformations 344
4 9 Matrix Representations for Linear Transformations 353
4 10 Change of Basis and Diagonalization 367
Determinants 379
5 1 Introduction 379
5 2 Cofactor Expansions of Determinants 380
5 3 Elementary Operations and Determinants 385
5 4 Cramer s Rule 395
5 5 Applications of Determinants: Inverses and Wronskians 402
Contents xi
Eigenvalues and Applications 413
6 1 Quadratic Forms 413
6 2 Systems of Differential Equations 424
6 3 Transformation to Hessenberg Form 433
6 4 Eigenvalues of Hessenberg Matrices 442
6 5 Householder Transformations 451
6 6 The QR Factorization and Least-Squares Solutions 463
6 7 Matrix Polynomials and the Cayley—Hamilton Theorem 473
6 8 Generalized Eigenvectors and Solutions of Systems
of Differential Equations 480
Numerical Methods in Linear Algebra 489
7 1 Computer Arithmetic and Roundoff (Optional) 489
7 2 Gaussian Elimination 494
7 3 The Power Method for Eigenvalues 504
7 4 The Inverse Power Method for the Eigenvalue Problem 512
7 5 Reduction to Hessenberg Form 519
7 6 Estimating the Eigenvalues of Hessenberg Matrices 523
Appendix: Review of Geometric Vectors 533
Answers to Odd-Numbered Exercises 539
Glossary of Symbols 571
Index 573
|
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| institution | BVB |
| isbn | 0201168332 |
| language | English |
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| physical | XI, 578 S. |
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| spelling | Johnson, Lee W. Verfasser aut Introduction to linear algebra Lee W. Johnson ; R. Dean Riess ; Jimmy T. Arnold 2. ed. Reading, Mass. u.a. Addison-Wesley 1989 XI, 578 S. txt rdacontent n rdamedia nc rdacarrier Algèbre linéaire Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 Riess, Ronald Dean 1940- Verfasser aut Arnold, Jimmy T. Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001208406&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Johnson, Lee W. Riess, Ronald Dean 1940- Arnold, Jimmy T. Introduction to linear algebra Algèbre linéaire Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4151278-9 |
| title | Introduction to linear algebra |
| title_auth | Introduction to linear algebra |
| title_exact_search | Introduction to linear algebra |
| title_full | Introduction to linear algebra Lee W. Johnson ; R. Dean Riess ; Jimmy T. Arnold |
| title_fullStr | Introduction to linear algebra Lee W. Johnson ; R. Dean Riess ; Jimmy T. Arnold |
| title_full_unstemmed | Introduction to linear algebra Lee W. Johnson ; R. Dean Riess ; Jimmy T. Arnold |
| title_short | Introduction to linear algebra |
| title_sort | introduction to linear algebra |
| topic | Algèbre linéaire Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Algebras, Linear Lineare Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001208406&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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