A course in linear algebra with applications:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2006
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 436 S. graph. Darst. |
| ISBN: | 9812700242 9812700234 |
Staff View
MARC
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| 245 | 1 | 0 | |a A course in linear algebra with applications |c Derek J. S. Robinson |
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Record in the Search Index
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| adam_text | Titel: A course in linear algebra with applications
Autor: Robinson, Derek John Scott
Jahr: 2006
CONTENTS
Preface to the Second Edition vii
Preface to the First Edition ix
Chapter One Matrix Algebra
1.1 Matrices 1
1.2 Operations with Matrices 6
1.3 Matrices over Rings and Fields 24
Chapter Two Systems of Linear Equations
2.1 Gaussian Elimination 30
2.2 Elementary Row Operations 41
2.3 Elementary Matrices 47
Chapter Three Determinants
3.1 Permutations and the Definition of a
Determinant 57
3.2 Basic Properties of Determinants 70
3.3 Determinants and Inverses of Matrices 78
xiii
xiv
Contents
Chapter Four Introduction to Vector Spaces
4.1 Examples of Vector Spaces 87
4.2 Vector Spaces and Subspaces 95
4.3 Linear Independence in Vector Spaces 104
Chapter Five Basis and Dimension
5.1 The Existence of a Basis 112
5.2 The Row and Column Spaces of a Matrix 126
5.3 Operations with Subspaces 133
Chapter Six Linear Transformations
6.1 Functions Defined on Sets 152
6.2 Linear Transformations and Matrices 158
6.3 Kernel, Image and Isomorphism 178
Chapter Seven Orthogonality in Vector Spaces
7.1 Scalar Products in Euclidean Space 193
7.2 Inner Product Spaces 209
7.3 Orthonormal Sets and the Gram-Schmidt
Process 226
7.4 The Method of Least Squares 241
Chapter Eight Eigenvectors and Eigenvalues
8.1 Basic Theory of Eigenvectors and Eigenvalues 257
8.2 Applications to Systems of Linear Recurrences 276
8.3 Applications to Systems of Linear Differential
Equations OQQ
Contents
XV
Chapter Nine More Advanced Topics
9.1 Eigenvalues and Eigenvectors of Symmetric and
Hermitian Matrices 303
9.2 Quadratic Forms 313
9.3 Bilinear Forms 332
9.4 Minimum Polynomials and Jordan Normal
Form 347
Chapter Ten Linear Programming
10.1 Introduction to Linear Programming 370
10.2 The Geometry of Linear Programming 380
10.3 Basic Solutions and Extreme Points 391
10.4 The Simplex Algorithm 399
Appendix Mathematical Induction 415
Answers to the Exercises 418
Bibliography 430
Index 432
|
| adam_txt |
Titel: A course in linear algebra with applications
Autor: Robinson, Derek John Scott
Jahr: 2006
CONTENTS
Preface to the Second Edition vii
Preface to the First Edition ix
Chapter One Matrix Algebra
1.1 Matrices 1
1.2 Operations with Matrices 6
1.3 Matrices over Rings and Fields 24
Chapter Two Systems of Linear Equations
2.1 Gaussian Elimination 30
2.2 Elementary Row Operations 41
2.3 Elementary Matrices 47
Chapter Three Determinants
3.1 Permutations and the Definition of a
Determinant 57
3.2 Basic Properties of Determinants 70
3.3 Determinants and Inverses of Matrices 78
xiii
xiv
Contents
Chapter Four Introduction to Vector Spaces
4.1 Examples of Vector Spaces 87
4.2 Vector Spaces and Subspaces 95
4.3 Linear Independence in Vector Spaces 104
Chapter Five Basis and Dimension
5.1 The Existence of a Basis 112
5.2 The Row and Column Spaces of a Matrix 126
5.3 Operations with Subspaces 133
Chapter Six Linear Transformations
6.1 Functions Defined on Sets 152
6.2 Linear Transformations and Matrices 158
6.3 Kernel, Image and Isomorphism 178
Chapter Seven Orthogonality in Vector Spaces
7.1 Scalar Products in Euclidean Space 193
7.2 Inner Product Spaces 209
7.3 Orthonormal Sets and the Gram-Schmidt
Process 226
7.4 The Method of Least Squares 241
Chapter Eight Eigenvectors and Eigenvalues
8.1 Basic Theory of Eigenvectors and Eigenvalues 257
8.2 Applications to Systems of Linear Recurrences 276
8.3 Applications to Systems of Linear Differential
Equations OQQ
Contents
XV
Chapter Nine More Advanced Topics
9.1 Eigenvalues and Eigenvectors of Symmetric and
Hermitian Matrices 303
9.2 Quadratic Forms 313
9.3 Bilinear Forms 332
9.4 Minimum Polynomials and Jordan Normal
Form 347
Chapter Ten Linear Programming
10.1 Introduction to Linear Programming 370
10.2 The Geometry of Linear Programming 380
10.3 Basic Solutions and Extreme Points 391
10.4 The Simplex Algorithm 399
Appendix Mathematical Induction 415
Answers to the Exercises 418
Bibliography 430
Index 432 |
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| index_date | 2024-07-02T16:40:57Z |
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| isbn | 9812700242 9812700234 |
| language | English |
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| spelling | Robinson, Derek John Scott 1938- Verfasser (DE-588)1017969213 aut A course in linear algebra with applications Derek J. S. Robinson 2. ed. Singapore [u.a.] World Scientific 2006 XV, 436 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lineaire algebra gtt Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4151278-9 Einführung 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=015466040&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robinson, Derek John Scott 1938- A course in linear algebra with applications Lineaire algebra gtt Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4151278-9 |
| title | A course in linear algebra with applications |
| title_auth | A course in linear algebra with applications |
| title_exact_search | A course in linear algebra with applications |
| title_exact_search_txtP | A course in linear algebra with applications |
| title_full | A course in linear algebra with applications Derek J. S. Robinson |
| title_fullStr | A course in linear algebra with applications Derek J. S. Robinson |
| title_full_unstemmed | A course in linear algebra with applications Derek J. S. Robinson |
| title_short | A course in linear algebra with applications |
| title_sort | a course in linear algebra with applications |
| topic | Lineaire algebra gtt Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineaire algebra Algebras, Linear Lineare Algebra Einführung |
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