A basis for linear algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Sydney
Wiley
1973
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 189 S.: graph.Darst. |
| ISBN: | 0471104604 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface vii
Notations viii
Chapter 0. A Note on Definitions, Postulates, Theorems and Proofs 1
Chapter 1. Some Mathematical Objects 7
§ 1. Matrices and Matrix Operations 7
§ 2. Finite Arithmetics (Modular Arithmetic) 11
§ 3. The Complex Numbers 13
§4. Functions, Maps and Permutations 16
Exercises for Chapter 1. 22
Chapter 2. Axiomatically Denned Systems:
Groups, Rings and Fields 26
§ 5. Axiomatics and Short Notation 26
§ 6. Isomorphisms of Algebraic Systems 32
Exercises for Chapter 2. 35
Chapter 3. Vector Spaces 37
§ 7. Elementary Notions and Examples 37
§ 8. Dimension: Linear Dependence and
Independence: Bases 44
§ 9. Subspaces 52
§10. Three Obvious Theorems about Dimension 56
§11. Expansion and Contraction to a Basis 57
Exercises for Chapter 3 61
Chapter 4. Homomorphisms of Vectorspaces 65
§12. Definitions and Examples 65
§13. Kernel and Image 67
§14. The Correspondence between Homomorphisms and
Matrices 71
Exercises for Chapter 4 79
vi Contents
Chapter 5. The Determinant and Inverses of Matrices 83
§15. Statement of the Problem 83
§15j. The General Case: Analysis and Guesses 84
§16. Properties of the Determinant and its Existence 85
§17. Algorithms for Producing the Determinant 90
§18. The Problem Solved 93
Exercises for Chapter 5 94
Chapter 6. Applications and Extensions of the Idea Vectorspace 98
§19. Applications of the Notions Kernel and Image 98
§19f Further Afield: Simple Linear Differential
Equations and Ideas of Kernel and Image 108
§20. Eigenvectors and Eigenvalues of a Matrix 109
§20i Usefulness of C rather than U 116
§21. Geometry: Ideas of Length and Orthogonality 117
§22. Complete Shifts of Axes on the Plane 122
§22j. The General Equation of Second Degree 125
Exercises for Chapter 6 130
Appendix One. Equivalence Relations, Equivalence Classes, and
Congruences 137
Appendix Two. Finite Induction 140
Exercises 144
Appendix Three. Equations in too many Unknowns 146
Appendix Four. Calculation of the Inverse of a Matrix 148
Appendix Five. Alternative Definition of the Determinant 151
Appendix Six. Parity of Permutations: Symmetric and
Alternating Groups 153
Appendix Seven. N / Q »R C 156
Appendix Eight. Calculations with Complex Numbers 160
Appendix Nine. A Few Facts About the Conies 166
Appendix Ten. Symbolic Logic Notation 169
Appendix Eleven. Botany : Some Named Algebraic Structures 173
Answers to Exercises 177
Index 187
|
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| dewey-ones | 512 - Algebra |
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| indexdate | 2024-07-09T16:35:34Z |
| institution | BVB |
| isbn | 0471104604 |
| language | English |
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| physical | VI, 189 S.: graph.Darst. |
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| spelling | Brisley, Warren Verfasser aut A basis for linear algebra Sydney Wiley 1973 VI, 189 S.: graph.Darst. txt rdacontent n rdamedia nc rdacarrier Algebra Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Vektorraum (DE-588)4130622-3 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 Vektorraum (DE-588)4130622-3 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=003655157&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 | Brisley, Warren A basis for linear algebra Algebra Lineare Algebra (DE-588)4035811-2 gnd Vektorraum (DE-588)4130622-3 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4130622-3 (DE-588)4151278-9 |
| title | A basis for linear algebra |
| title_auth | A basis for linear algebra |
| title_exact_search | A basis for linear algebra |
| title_full | A basis for linear algebra |
| title_fullStr | A basis for linear algebra |
| title_full_unstemmed | A basis for linear algebra |
| title_short | A basis for linear algebra |
| title_sort | a basis for linear algebra |
| topic | Algebra Lineare Algebra (DE-588)4035811-2 gnd Vektorraum (DE-588)4130622-3 gnd |
| topic_facet | Algebra Lineare Algebra Vektorraum Einführung |
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