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 Wayne |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
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| 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
|
| adam_txt |
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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| institution | BVB |
| isbn | 0805383050 |
| language | English |
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| publisher | Benjamin Cummings |
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| spelling | Roberts, Arthur Wayne 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 (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=015096885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roberts, Arthur Wayne 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_exact_search_txtP | 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 |
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