Lineare Algebra und Geometrie:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1992
|
| Edition: | 3. Aufl. |
| Series: | Springer-Lehrbuch
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 293 S. graph. Darst. |
| ISBN: | 3540556737 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804119782905085952 |
|---|---|
| adam_text | Inhaltsverzeichnis
1 Allgemeine Grundbegriffe
1.1 Mengen und Abbildungen 1
1.2 Gruppen 3
1.3 Gruppenmorphismen 5
1.4 Äquivalenzrelationen und Quotientengruppen 7
1.5 Ringe und Körper 11
2 Vektorräume
2.1 Moduln und Vektorräume 17
2.2 Lineare Abbildungen 19
2.3 Erzeugendensysteme und freie Systeme 21
2.4 Basissysteme 24
2.5 Endlichdimensionale Vektorräume 26
2.6 Lineare Komplemente 28
3 Matrizen
3.1 Vektorräume linearer Abbildungen 33
3.2 Dualräume 34
3.3 Die transponierte Abbildung 38
3.4 Matrizen 41
3.5 Das Matrizenprodukt 44
3.6 Der Rang 47
4 Lineare Gleichungen und Determinanten
4.1 Lineare Gleichungssysteme 53
4.2 Das Gaußsche Eliminationsverfahren 55
4.3 Die symmetrische Gruppe 58
4.4 Determinanten 60
4.5 Der Determinantenentwicklungssatz 65
¦^H Inhaltsverzeichnis
5 Eigenwerte und Normalformen
5.1 Eigenwerte 71
5.2 Normalformen. Elementare Theorie 74
5.3 Der Satz von Hamilton Cayley 77
5.4 Die Jordan Normalform 79
5.5 Lineare Differentialgleichungssysteme mit
konstanten Koeffizienten (komplexer Fall) 85
5.6 Die Jordan Normalform über 1R 87
5.7 Lineare Differentialgleichungssysteme mit
konstanten Koeffizienten (reeller Fall) 91
6 Metrische Vektorräume
6.1 Unitäre Vektorräume 97
6.2 Normierte Vektorräume 102
6.3 Hilberträume 108
6.4 Lineare Operatoren. Die unitäre Gruppe 114
6.5 Hermitesche Formen 121
7 Affine Geometrie
7.1 Der affine Raum 129
7.2 Affinitäten und Kollineationen. Der Fundamentalsatz 134
7.3 Lineare Funktionen 139
7.4 Affine Quadriken 145
8 Euklidische Geometrie
8.1 Der affin unitäre Raum 159
8.2 Lineare und quadratische Funktionen 164
8.3 Der Winkel 170
8.4 Anhang: Quaternionen und SO (3), SO (4) 177
8.5 Dreieckslehre 181
8.6 Kegelschnitte 189
9 Projektive Geometrie
9.1 Der projektive Raum 207
9.2 Die projektive Erweiterung eines affinen Raumes 210
9.3 Anhang: Allgemeine projektive und affine Ebenen 217
9.4 Das Doppelverhältnis. Der Satz von v. Staudt 223
9.5 Quadriken und Polaritäten 231
Inhaltsverzeichnis XIII
10 Nichteuklidische Geometrie
10.1 Der hyperbolische Raum 243
10.2 Das konforme Modell des hyperbolischen Raumes 250
10.3 Elliptische Geometrie 262
10.4 Das konforme Modell des elliptischen Raumes 266
10.5 Cliffordparallelen 272
10.6 Sphärische Geometrie und Dreieckslehre 277
Literaturhinweise 283
Literaturverzeichnis 285
Index 287
|
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| classification_rvk | SK 110 SK 220 |
| classification_tum | MAT 150f MAT 516f |
| ctrlnum | (OCoLC)31920273 (DE-599)BVBBV005568422 |
| discipline | Mathematik |
| edition | 3. Aufl. |
| format | Book |
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| genre_facet | Einführung |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:31:40Z |
| institution | BVB |
| isbn | 3540556737 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003489297 |
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| physical | XIII, 293 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer-Lehrbuch |
| spelling | Klingenberg, Wilhelm 1924-2010 Verfasser (DE-588)119135884 aut Lineare Algebra und Geometrie Wilhelm Klingenberg 3. Aufl. Berlin [u.a.] Springer 1992 XIII, 293 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer-Lehrbuch Algebras, Linear Geometry Geometrie (DE-588)4020236-7 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Analytische Geometrie (DE-588)4001867-2 s DE-604 Lineare Algebra (DE-588)4035811-2 s Geometrie (DE-588)4020236-7 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=003489297&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 | Klingenberg, Wilhelm 1924-2010 Lineare Algebra und Geometrie Algebras, Linear Geometry Geometrie (DE-588)4020236-7 gnd Lineare Algebra (DE-588)4035811-2 gnd Analytische Geometrie (DE-588)4001867-2 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4035811-2 (DE-588)4001867-2 (DE-588)4151278-9 |
| title | Lineare Algebra und Geometrie |
| title_auth | Lineare Algebra und Geometrie |
| title_exact_search | Lineare Algebra und Geometrie |
| title_full | Lineare Algebra und Geometrie Wilhelm Klingenberg |
| title_fullStr | Lineare Algebra und Geometrie Wilhelm Klingenberg |
| title_full_unstemmed | Lineare Algebra und Geometrie Wilhelm Klingenberg |
| title_short | Lineare Algebra und Geometrie |
| title_sort | lineare algebra und geometrie |
| topic | Algebras, Linear Geometry Geometrie (DE-588)4020236-7 gnd Lineare Algebra (DE-588)4035811-2 gnd Analytische Geometrie (DE-588)4001867-2 gnd |
| topic_facet | Algebras, Linear Geometry Geometrie Lineare Algebra Analytische Geometrie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003489297&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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