Linear algebra: an introductory approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1993
|
| Ausgabe: | Corr. 4. print. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 337 S. graph. Darst. |
| ISBN: | 3540909923 0387909923 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1823026239035670528 |
|---|---|
| adam_text |
CHARLES W. CURTIS
LINEAR ALGEBRA
AN
INTRODUCTORY APPROACH
WITH 37 ILLUSTRATIONS
SPRINGER-VERLAG
NEW
YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO
HONGKONG BARCELONA BUDAPEST
CONTENTS
1.
INTRODUCTION TO LINEAR ALGEBRA 1
1.
SOME PROBLEMS WHICH LEAD TO LINEAR ALGEBRA 1
2.
NUMBER SYSTEMS AND MATHEMATICAL INDUCTION 6
2.
VECTOR SPACES AND SYSTEMS OF LINEAR EQUATIONS 16
3.
VECTOR SPACES 16
4.
SUBSPACES AND LINEAR DEPENDENCE 26
5.
THE CONCEPTS OF BASIS AND DIMENSION 34
6.
ROW EQUIVALENCE OF MATRICES 38
7.
SOME GENERAL THEOREMS ABOUT FINITELY GENERATED VECTOR
SPACES 48
8.
SYSTEMS OF LINEAR EQUATIONS 53
9.
SYSTEMS OF HOMOGENEOUS EQUATIONS 62
10.
LINEAR MANIFOLDS 69
3.
LINEAR TRANSFORMATIONS AND MATRICES 75
11
.
LINEAR TRANSFORMATIONS 75
12.
ADDITION AND MULTIPLICATION OF MATRICES 88
13.
LINEAR TRANSFORMATIONS AND MATRICES 99
4.
VECTOR SPACES WITH AN INNER PRODUCT 109
14.
THE CONCEPT OF SYMMETRY 109
15.
INNER PRODUCTS 119
IX
X
CONTENTS
5. DETERMINANTS 132
16.
DEFINITION OF DETERMINANTS 132
17.
EXISTENCE AND UNIQUENESS OF DETERMINANTS 140
18.
THE MULTIPLICATION THEOREM FOR DETERMINANTS 146
19.
FURTHER PROPERTIES OF DETERMINANTS 150
6. POLYNOMIALS AND COMPLEX NUMBERS 163
20.
POLYNOMIALS 163
21.
COMPLEX NUMBERS 176
7. THE THEORY OF
A
SINGLE LINEAR TRANSFORMATION 184
22.
BASIC CONCEPTS 184
23.
INVARIANT SUBSPACES 193
24.-
THE TRIANGULAER FORM THEOREM 201
25.
THE RATIONAL AND JORDAN CANONICAL FORMS 216
8. DUAL VECTOR SPACES AND MULTILINEAR ALGEBRA 228
26.
QUOTIENT SPACES AND DUAL VECTOR SPACES 228
27.
BILINEAR FORMS AND DUALITY 236
28.
DIRECT SUMS AND TENSOR PRODUCTS 243
29.
A PROOF OF THE ELEMENTARY DIVISOR THEOREM 260
9. ORTHOGONAL AND UNITARY TRANSFORMATIONS 266
30.
THE STRUCTURE OF ORTHOGONAL TRANSFORMATIONS 266
31.
THE PRINCIPAL AXIS THEOREM 271
32.
UNITARY TRANSFORMATIONS AND THE SPECTRAL THEOREM 278
10.
SOME APPLICATIONS OF LINEAR ALGEBRA 289
33.
FINITE SYMMETRY GROUPS IN THREE DIMENSIONS 289
34.
APPLICATION TO DIFFERENTIAL EQUATIONS 298
35.
SUMS OF SQUARES AND HURWITZ'S THEOREM 306
BIBLIOGRAPHY (WITH NOTES)
315
SOLUTIONS OF SELECTED EXERCISES
317
SYMBOLS (INCLUDING GREEK LETTERS)
332
INDEX
334 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 150f |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 19 |
| dewey-search | 512/.55 19 |
| dewey-sort | 3512 255 219 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 4. print. |
| format | Book |
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| indexdate | 2025-02-03T09:01:40Z |
| institution | BVB |
| isbn | 3540909923 0387909923 |
| language | English |
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| spelling | Curtis, Charles W. 1926- Verfasser (DE-588)110295552 aut Linear algebra an introductory approach Charles W. Curtis Corr. 4. print. New York u.a. Springer 1993 X, 337 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Algebras, Linear 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=006051534&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 |
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| subject_GND | (DE-588)4035811-2 (DE-588)4151278-9 |
| title | Linear algebra an introductory approach |
| title_auth | Linear algebra an introductory approach |
| title_exact_search | Linear algebra an introductory approach |
| title_full | Linear algebra an introductory approach Charles W. Curtis |
| title_fullStr | Linear algebra an introductory approach Charles W. Curtis |
| title_full_unstemmed | Linear algebra an introductory approach Charles W. Curtis |
| title_short | Linear algebra |
| title_sort | linear algebra an introductory approach |
| title_sub | an introductory approach |
| topic | Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Lineare Algebra Einführung |
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