Introduction to linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
[1991]
|
| Edition: | 2. ed., [Nachdr.] |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 293 S. graph. Darst. |
| ISBN: | 0387962050 3540962050 |
Staff View
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Record in the Search Index
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| adam_text |
SERGE LANG
INTRODUCTION
TO
LINEAR ALGEBRA
SECOND EDITION
WITH 66 ILLUSTRATIONS
SPRINGER-VERLAG
NEW
YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO
HONG KONG BARCELONA BUDAPEST
CONTENTS
CHAPTER I
VECTORS
1
§1.
DEFINITION OF POINTS IN SPACE 1
§2.
LOCATED VECTORS 9
§3.
SCALAR PRODUCT , 12
§4.
THE NORM OF A VECTOR 15
§5.
PARAMETRIC LINES 30
§6.
PLANES 34
CHAPTER
TI
MATRICES
AND LINEAR EQUATIONS 42
§1.
MATRICES 43
§2.
MULTIPLICATION OF MATRICES 47
§3.
HOMOGENEOUS LINEAR EQUATIONS AND ELIMINATION 64
§4.
ROW OPERATIONS AND GAUSS ELIMINATION 70
§5 ROW OPERATIONS AND ELEMENTARY MATRICES 77
§6.
LINEAR COMBINATIONS 85
CHAPTER III
VECTOR
SPACES 88
§1.
DEFINITIONS 88
§2.
LINEAR COMBINATIONS 93
§3.
CONVEX SETS 99
§4.
LINEAR INDEPENDENCE 104
§5.
DIMENSION 110
§6.
THE RANK OF A MATRIX 115
VLLL
CONTENTS
CHAPTER IV
LINEAR MAPPINGS 123
§1.
MAPPINGS 123
§2.
LINEAR MAPPINGS 127
§3.
THE KERNEL AND IMAGE OF A LINEAR MAP 136
§4.
THE RANK AND LINEAR EQUATIONS AGAIN 144
§5.
THE MATRIX ASSOCIATED WITH A LINEAR MAP 150
APPENDIX: CHANGE OF BASES 154
CHAPTER V
COMPOSITION
AND INVERSE MAPPINGS 158
§1.
COMPOSITION OF LINEAR MAPS 158
§2.
INVERSES 164
CHAPTER VI
SCALAR
PRODUCTS AND ORTHOGONALITY 171
§1.
SCALAR PRODUCTS 171
§2.
ORTHOGONAL BASES 180
§3.
BILINEAR MAPS AND MATRICES 190
CHAPTER VII
DETERMINANTS
195
§1.
DETERMINANTS OF ORDER 2 195
§2.
3 X 3 AND
N X N
DETERMINANTS 200
§3.
THE RANK OF A MATRIX AND SUBDETERMINANTS 210
§4.
CRAMER'S RULE 214
§5.
INVERSE OF A MATRIX 217
§6.
DETERMINANTS AS AREA AND VOLUME 221
CHAPTER VIII
EIGENVECTORS
AND EIGENVALUES 233
§1.
EIGENVECTORS AND EIGENVALUES 233
§2.
THE CHARACTERISTIC POLYNOMIAL 238
§3.
EIGENVALUES AND EIGENVECTORS OF SYMMETRIC MATRICES 250
§4.
DIAGONALIZATION OF A SYMMETRIC LINEAR MAP 255
APPENDIX. COMPLEX NUMBERS 260
ANSWERS TO EXERCISES 266
INDEX
291 |
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| index_date | 2024-07-02T19:20:37Z |
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| isbn | 0387962050 3540962050 |
| language | English |
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| physical | VIII, 293 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
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| publisher | Springer |
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| series2 | Undergraduate texts in mathematics |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Introduction to linear algebra Serge Lang 2. ed., [Nachdr.] New York [u.a.] Springer [1991] VIII, 293 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Lineare Algebra (DE-588)4035811-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244479&sequence=000001&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 | Lang, Serge 1927-2005 Introduction to linear algebra Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4151278-9 |
| title | Introduction to linear algebra |
| title_auth | Introduction to linear algebra |
| title_exact_search | Introduction to linear algebra |
| title_exact_search_txtP | Introduction to linear algebra |
| title_full | Introduction to linear algebra Serge Lang |
| title_fullStr | Introduction to linear algebra Serge Lang |
| title_full_unstemmed | Introduction to linear algebra Serge Lang |
| title_short | Introduction to linear algebra |
| title_sort | introduction to linear algebra |
| topic | Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineare Algebra Einführung |
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