Introduction to linear and abstract Algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Glenview, Ill.
Scott, Foresman
1971
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 415 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to linear and abstract Algebra |c Robert C. Thompson ; Adil Yaqub |
| 264 | 1 | |a Glenview, Ill. |b Scott, Foresman |c 1971 | |
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Datensatz im Suchindex
| _version_ | 1804119896891588608 |
|---|---|
| adam_text | CONTENTS
Chapter 1 INTRODUCTORY TOPICS
1.1 Introduction
1.2 Sets 1
1.3 Functions 5
1.4 Equivalence Relations 15
Chapter 2 RINGS AND FIELDS
2.1 Introduction
2.2 Rings 21
2.3 Elementary Properties of Rings 29
2.4 Fields 38
2.5 The Real and the Complex Numbers 43
Chapter 3 VECTOR SPACES
3.1 Introduction
3.2 Definition and Examples of Vector Spaces 51
3.3 Basis and Dimension 66
3.4 Subspaces 77
3.5 Isomorphisms of Vector Spaces 87
Chapter 4 LINEAR TRANSFORMATIONS AND MATRICES
4.1 Introduction
4.2 Linear Transformations 91
4.3 The Algebra of Linear Transformations 100
4.4 Linear Transformations and Matrices 110
4.5 The Algebra of Matrices 118
Chapter 5 RANK AND SYSTEMS OF LINEAR EQUATIONS
5.1 Introduction
5.2 Row and Column Spaces 135
5.3 Systems of Linear Equations 147
Chapter 6 INTEGERS AND POLYNOMIALS
6.1 Introduction
6.2 Polynomial Rings 157
6.3 Divisibility and Related Topics 166
6.4 Roots of Polynomials 178
Chapter 7 RINGS AND IDEALS
7.1 Introduction
7.2 Ideals 191
7.3 Residue Class Rings 202
7.4 Prime and Maximal Ideals 216
7.5 The Existence of Roots of Polynomials 221
Chapter 8 GROUP THEORY
8.1 Introduction
8.2 Definition and Examples of Groups 227
8.3 Elementary Properties of Groups 233
8.4 Subgroups 238
8.5 Cyclic Groups 245
8.6 Permutation Groups 255
8.7 Homomorphisms and Isomorphisms of Groups 263
Chapter 9 FIELD THEORY
9.1 Introduction
9.2 The Field of Fractions 273
9.3 Prime Fields and Extension Fields 284
9.4 The Determination of All Finite Fields 291
Chapter 10 DETERMINANTS
10.1 Introduction
10.2 Determinants 297
10.3 Expansion Theorems 307
10.4 Determinantal Rank 314
Chapter 11 INTRODUCTION TO EIGENVALUE THEORY
11.1 Introduction
11.2 An Example 317
11.3 Extension of the Field 320
11.4 Similarity of Matrices 325
11.5 Eigenvalues and Eigenvectors 328
11.6 Diagonal Representations
of Linear Transformations 333
Chapter 12 INNER PRODUCT SPACES
12.1 Introduction
12.2 Lengths, Angles, and Inner Products
in Three Dimensions 339
12.3 Inner Products in Abstract Vector Spaces 342
12.4 Orthonormal Basis 348
12.5 Orthogonal Complements 354
Chapter 13 LINEAR TRANSFORMATIONS
ON INNER PRODUCT SPACES
13.1 Introduction
13.2 The Adjoint 357
13.3 Orthogonal Linear Transformations 362
13.4 Symmetric Linear Transformations 367
Appendix 1 Inequalities and Absolute Value 371
Appendix 2 Proof by Induction 372
Appendix 3 The Binomial Theorem 375
Appendix 4 The Fundamental Theorem of Algebra 378
ANSWERS TO SELECTED EXERCISES 383
SYMBOLS AND NOTATIONS 406
INDEX 409
|
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.5 |
| dewey-search | 512/.5 |
| dewey-sort | 3512 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:33:29Z |
| institution | BVB |
| language | English |
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| physical | 415 S. graph. Darst. |
| publishDate | 1971 |
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| spelling | Thompson, Robert C... 1931-1995 Verfasser (DE-588)117726206 aut Introduction to linear and abstract Algebra Robert C. Thompson ; Adil Yaqub Glenview, Ill. Scott, Foresman 1971 415 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algebra, Abstract Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Universelle Albegra gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 Algebraische Struktur (DE-588)4001166-5 s Universelle Albegra f Yaqub, Adil 1928- Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003567460&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thompson, Robert C... 1931-1995 Yaqub, Adil 1928- Introduction to linear and abstract Algebra Algebra, Abstract Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4001166-5 (DE-588)4151278-9 |
| title | Introduction to linear and abstract Algebra |
| title_auth | Introduction to linear and abstract Algebra |
| title_exact_search | Introduction to linear and abstract Algebra |
| title_full | Introduction to linear and abstract Algebra Robert C. Thompson ; Adil Yaqub |
| title_fullStr | Introduction to linear and abstract Algebra Robert C. Thompson ; Adil Yaqub |
| title_full_unstemmed | Introduction to linear and abstract Algebra Robert C. Thompson ; Adil Yaqub |
| title_short | Introduction to linear and abstract Algebra |
| title_sort | introduction to linear and abstract algebra |
| topic | Algebra, Abstract Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| topic_facet | Algebra, Abstract Algebras, Linear Lineare Algebra Algebraische Struktur Einführung Universelle Albegra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003567460&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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