Introduction to matrices and linear transformations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Francisco
Freeman
1978
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | A series of books in the mathematical sciences.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 462 S. |
| ISBN: | 0716700840 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804116713136979968 |
|---|---|
| adam_text | CONTENTS
CHAPTER 1
LINEAR EQUATIONS 1
1.1 Systems of Linear Equations 2
1.2 Matrix Representation of a Linear System 11
1.3 Solutions of a Linear System 19
CHAPTER 2
LINEAR SPACES 25
2.1 Vector Algebra in W 25
2.2 Euclidean n Space 32
2.3 Vector Spaces 39
2.4 Subspaces 45
2.5 Linear Independence 54
2.6 Bases and Dimension 60
2.7 Isomorphisms of Vector Spaces 66
IX
x CONTENTS
CHAPTER 3
LINEAR MAPPINGS 73
3.1 Algebra of Homomorphisms 73
3.2 Rank and Nullity of a Linear Mapping 82
3.3 Nonsingular Mappings 88
3.4 Matrix Representation of a Linear Mapping 92
CHAPTER 4
MATRICES 101
4.1 Algebra of Matrices 101
4.2 Special Types of Square Matrices 110
4.3 Elementary Matrices 116
4.4 Rank of a Matrix 124
4.5 Geometry of Linear Systems 129
4.6 Block Multiplication of Matrices 132
CHAPTER 5
DETERMINANTS 138
5.1 Basic Properties of Determinants 138
5.2 An Explicit Formula for det A 145
5.3 Some Applications of Determinants 154
CHAPTER 6
EQUIVALENCE RELATIONS ON RECTANGULAR
MATRICES 161
6.1 Row Equivalence 161
6.2 Change of Basis 166
6.3 Equivalence 173
6.4 Similarity 178
CHAPTER 7
A CANONICAL FORM FOR SIMILARITY 185
7.1 Characteristic Values and Vectors 185
7.2 Diagonability 193
Contents xi
7.3 Invariant Subspaces 203
7.4 The Minimal Polynomial 208
7.5 Nilpotent Transformations 215
7.6 Jordan Canonical Form 221
7.7 Reduction to Jordan Form 228
7.8 An Application of the Hamilton Cayley Theorem 235
CHAPTER 8
INNER PRODUCT SPACES 241
8.1 Inner Products 241
8.2 Length, Distance, Orthogonality 247
8.3 Isometries 255
CHAPTER 9
SCALAR VALUED FUNCTIONS 261
9.1 Linear Functionals 261
9.2 Transpose of a Linear Mapping 266
9.3 Bilinear Functions 270
9.4 Conjunctivity and Congruence 276
9.5 Hermitian and Quadratic Functions 283
9.6 Isometric Diagonability 296
CHAPTER 10
APPLICATION: LINEAR PROGRAMMING 306
10.1 Linear Inequalities 307
10.2 Dual Linear Programs 315
10.3 Computational Techniques 323
10.4 Simplex Method 333
CHAPTER 11
APPLICATION: LINEAR DIFFERENTIAL
EQUATIONS 344
11.1 Sequences and Series of Matrices 344
11.2 Matrix Power Series 349
xii CONTENTS
11.3 Matrices of Functions 357
11.4 Systems of Linear Differential Equations 361
APPENDIX A 371
A.1 Algebraic Systems and Fields 371
A.2 Sets and Subsets 374
A.3 Relations and Equivalence Relations 378
A.4 Functions and Operations 380
A.5 Complex Numbers 383
SOLUTIONS FOR SELECTED EXERCISES 387
INDEX 455
i
|
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| dewey-full | 512.9/43 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/43 |
| dewey-search | 512.9/43 |
| dewey-sort | 3512.9 243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV002256340 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:53Z |
| institution | BVB |
| isbn | 0716700840 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001482709 |
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| physical | XII, 462 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Freeman |
| record_format | marc |
| series2 | A series of books in the mathematical sciences. |
| spelling | Finkbeiner, Daniel T. Verfasser aut Introduction to matrices and linear transformations 3. ed. San Francisco Freeman 1978 XII, 462 S. txt rdacontent n rdamedia nc rdacarrier A series of books in the mathematical sciences. Algebras, Linear Matrices Lineare Transformation (DE-588)4167712-2 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Matrix Mathematik (DE-588)4037968-1 s Lineare Transformation (DE-588)4167712-2 s DE-604 Lineare Algebra (DE-588)4035811-2 s Matrizenrechnung (DE-588)4126963-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482709&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 | Finkbeiner, Daniel T. Introduction to matrices and linear transformations Algebras, Linear Matrices Lineare Transformation (DE-588)4167712-2 gnd Matrix Mathematik (DE-588)4037968-1 gnd Matrizenrechnung (DE-588)4126963-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4167712-2 (DE-588)4037968-1 (DE-588)4126963-9 (DE-588)4035811-2 (DE-588)4151278-9 |
| title | Introduction to matrices and linear transformations |
| title_auth | Introduction to matrices and linear transformations |
| title_exact_search | Introduction to matrices and linear transformations |
| title_full | Introduction to matrices and linear transformations |
| title_fullStr | Introduction to matrices and linear transformations |
| title_full_unstemmed | Introduction to matrices and linear transformations |
| title_short | Introduction to matrices and linear transformations |
| title_sort | introduction to matrices and linear transformations |
| topic | Algebras, Linear Matrices Lineare Transformation (DE-588)4167712-2 gnd Matrix Mathematik (DE-588)4037968-1 gnd Matrizenrechnung (DE-588)4126963-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Matrices Lineare Transformation Matrix Mathematik Matrizenrechnung Lineare Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482709&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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