Elementary linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. u.a.
Benjamin/Cummings
1985
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 414 S. graph. Darst. |
| ISBN: | 0805383050 |
Staff View
MARC
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| 100 | 1 | |a Roberts, Arthur W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elementary linear algebra |c A. Wayne Roberts |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Reading, Mass. u.a. |b Benjamin/Cummings |c 1985 | |
| 300 | |a XV, 414 S. |b graph. Darst. | ||
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| 650 | 4 | |a Algèbre linéaire | |
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Record in the Search Index
| _version_ | 1804120790998712320 |
|---|---|
| adam_text | CONTENTS
Every section ends with a problem set, and every chapter ends with a self-test.
FOREWORD by Victor Klee ix
PREFACE xi
1 SYSTEMS OF LINEAR EQUATIONS l
1-1 Introduction 1
1-2 Equivalent Systems of Equations 3
Vignette: Back to Basics 10
1-3 Gaussian Elimination 13
Vignette: Rough Approximations Can Become
Lumpy 16
1-4 Row Echelon Form 21
Vignette: Kirchhoff s Laws 28
2 THE SOLUTION SET FOR A LINEAR
SYSTEM 34
2-1 Introduction 34
2-2 Vectors in R 35
Vignette: A Geometric Proof 44
2-3 Dot Products and Projections 48
Vignette: Who Needs n Dimensions? 55
2-4 Spanning Sets 57
Vignette: A Balancing Act 66
2-5 Multiplication of Matrices 70
Vignette: Petrified Matrices 74
2-6 The Algebra of Matrices 78
Vignette: Information Please 80
Vignette: Not the Only Way to Fly 84
2-7 The Inverse of a Matrix 88
Vignette: Raisins for a Leontief Production
Model 93
Vignette: Giving You a Line 94
2-8 Describing the Solution Set 99
Vignette: Transportation Problems 106
3 DETERMINANTS ill
3-1 Introduction 111
3-2 Some Definitions 113
Vignette: Even and Odd Permutations 118
3-3 Properties of Determinants 127
Vignette: An Application to Ranks 134
3-4 Applications 137
Vignette: Lest We Forget 146
4 VECTORS AND VECTOR SPACES 152
4-1 Introduction 152
4-2 Vector Spaces 152
Vignette: Room for Imagination 159
Vignette: Some Significant
Observations 161
4-3 The Span of a Set 164
Vignette: Barycentric Coordinates 170
4-4 Bases and the Dimension of a Space 174
Vignette: Simpson s Rule 177
4-5 Inner Product Spaces 181
Vignette: Boxed in with the CBS
Inequality 184
4-6 Orthonormal Sets 188
Vignette: A Step Toward Fourier
Series 190
5 LINEAR TRANSFORMATIONS 200
5-1 Introduction 200
5-2 Definitions 203
Vignette: Transformed Areas 209
5-3 Matrix Representations of a Linear
Transformation 212
Vignette: The Derivative as a Linear
Transformation 220
5-4 Coordinates and Bases 225
Vignette: The Correct Basis Can Make It
Crystal Clear 234
5-5 Change of Basis 239
Vignette: Standard but Not Best 246
5-6 The Null Space and the Range 251
6 SQUARE MATRICES 259
6-1 Introduction 259
6-2 Eigenvalues and Eigenvectors 260
Vignette: A Method That Allows
Mistakes 266
6-3 Diagonalization of Symmetric Matrices 270
Vignette: Second Derivatives and Symmetric
Matrices 275
6-4 Quadratic Forms 277
Vignette: In variance in the Face of
Revolution 284
6-5 Positive Matrices 287
Vignette: Minimums for Functions of
Several Variables 290
6-6 Nonsymmetric Matrices 292
Vignette: Chipping Away: A Method with
Powers 294
Vignette: The Fibonacci Sequence 298
7 LINEAR PROGRAMMING 305
7-1 Introduction 305
7-2 A Geometric Approach 308
7-3 Extreme Points 319
7-4 The Simplex Method, Phase II 326
7-5 The Simplex Method, Phase I 333
8 MARKOV CHAINS 340
8-1 Introduction 340
8-2 The Powers of the Transition Matrix 342
8-3 Regular Markov Chains 350
8-4 Absorbing Markov Chains 356
9 DIFFERENTIAL EQUATIONS 367
9-1 Introduction 367
9-2 Linear Homogeneous Differential Equations
with Constant Coefficients 368
9-3 A Basis for the Solution Space 372
9-4 The Nonhomogeneous Case 378
9-5 Systems of Linear Differential
Equations 384
ANSWERS TO ODD-NUMBERED
PROBLEMS AND SELF-TESTS 390
INDEX 409
|
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| dewey-sort | 3512 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
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| genre_facet | Aufgabensammlung |
| id | DE-604.BV006525098 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:47:42Z |
| institution | BVB |
| isbn | 0805383050 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004155236 |
| oclc_num | 11260113 |
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| physical | XV, 414 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Benjamin/Cummings |
| record_format | marc |
| spelling | Roberts, Arthur W. Verfasser aut Elementary linear algebra A. Wayne Roberts 2. ed. Reading, Mass. u.a. Benjamin/Cummings 1985 XV, 414 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algèbre linéaire Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004155236&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 | Roberts, Arthur W. Elementary linear algebra Algèbre linéaire Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4143389-0 |
| title | Elementary linear algebra |
| title_auth | Elementary linear algebra |
| title_exact_search | Elementary linear algebra |
| title_full | Elementary linear algebra A. Wayne Roberts |
| title_fullStr | Elementary linear algebra A. Wayne Roberts |
| title_full_unstemmed | Elementary linear algebra A. Wayne Roberts |
| title_short | Elementary linear algebra |
| title_sort | elementary linear algebra |
| topic | Algèbre linéaire Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Algebras, Linear Lineare Algebra Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004155236&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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