Linear geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Heidelberg ; Berlin
Springer
[1977]
|
| Edition: | 2nd edition |
| Series: | Graduate texts in mathematics.
49 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 198 Seiten Illustrationen |
| ISBN: | 3540902279 0387902279 |
Staff View
MARC
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| 100 | 1 | |a Gruenberg, Karl W. |d 1928-2007 |0 (DE-588)107407612 |4 aut | |
| 245 | 1 | 0 | |a Linear geometry |c K. W. Gruenberg ; A. J. Weir |
| 250 | |a 2nd edition | ||
| 264 | 1 | |a New York ; Heidelberg ; Berlin |b Springer |c [1977] | |
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| 490 | 1 | |a Graduate texts in mathematics. |v 49 | |
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Record in the Search Index
| _version_ | 1804116700181823488 |
|---|---|
| adam_text | Contents
Guide
to the
Reader ix
ι
з
б
8
12
15
15
17
20
22
29
32
38
42
42
44
49
52
54
58
62
vii
Chapter I
Vector Spaces
1.1
Sets
1.2
Groups, Fields and Vector Spaces
1.3
Subspaces
1.4
Dimension
1.5
The Ground Field
Chapter II
Affine
and
Projective
Geometry
2.1
Affine
Geometries
2.2
Affine
Propositions of Incidence
2.3
Affine
Isomorphisms
2.4
Homogeneous Vectors
2.5
Projective
Geometries
2.6
The Embedding of
Affine
Geometry in
Projective
Geometry
2.7
The Fundamental Incidence Theorems of
Projective
Geometry
Chapter III
Isomorphisms
3.1
Affinities
3.2
Projectivities
3.3
Linear Equations
3.4
Affine
and
Projective
Isomorphisms
3.5
Semi-linear Isomorphisms
3.6
Groups of Automorphisms
3.7
Central Collineations
Contents
Chapter IV
Linear Mappings
66
4.1
Elementary Properties of Linear Mappings
66
4.2
Degenerate Affinities and Projectivities
70
4.3
Matrices
71
4.4
The Rank of a Linear Mapping
75
4.5
Linear Equations
79
4.6
Dual Spaces
80
4.7
Dualities
83
4.8
Dual Geometries
86
Chapter V
Bilinear Forms
89
5.1
Elementary Properties of Bilinear Forms
89
5.2
Orthogonality
93
5.3
Symmetric and Alternating Bilinear Forms
97
5.4
Structure Theorems
102
5.5
Correlations
110
5.6
Projective
Quadrics
111
5.7 Affine
Quadrics
115
5.8
Sesquilinear Forms
120
Chapter VI
Euclidean Geometry
125
6.1
Distances and Euclidean Geometries
125
6.2
Similarity Euclidean Geometries
130
6.3
Euclidean Quadrics
134
6.4
Euclidean Automorphisms
140
6.5
Hubert Spaces
146
Chapter
VII
Modules
149
7.1
Rings and Modules
149
7.2
Submodules
and Homomorphisms
153
7.3
Direct Decompositions
155
7.4
Equivalence of Matrices over F[X]
163
7.5
Similarity of Matrices over
F
166
7.6
Classification of Collineations
170
Solutions
175
List of Symbols
188
Bibliography
191
Index
193
viii
|
| any_adam_object | 1 |
| author | Gruenberg, Karl W. 1928-2007 Weir, Alan J. |
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| author_role | aut aut |
| author_sort | Gruenberg, Karl W. 1928-2007 |
| author_variant | k w g kw kwg a j w aj ajw |
| building | Verbundindex |
| bvnumber | BV002244225 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA564 |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd edition |
| format | Book |
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| id | DE-604.BV002244225 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:42:40Z |
| institution | BVB |
| isbn | 3540902279 0387902279 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001474865 |
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| physical | x, 198 Seiten Illustrationen |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics. |
| series2 | Graduate texts in mathematics. |
| spelling | Gruenberg, Karl W. 1928-2007 (DE-588)107407612 aut Linear geometry K. W. Gruenberg ; A. J. Weir 2nd edition New York ; Heidelberg ; Berlin Springer [1977] © 1977 x, 198 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics. 49 Algèbre linéaire Géométrie algébrique Lineaire algebra gtt Meetkunde gtt Algebras, Linear Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Lineare Geometrie (DE-588)4181966-4 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Algebraische Geometrie (DE-588)4001161-6 s DE-604 Lineare Algebra (DE-588)4035811-2 s Lineare Geometrie (DE-588)4181966-4 s 1\p DE-604 Weir, Alan J. (DE-588)108783049 aut Erscheint auch als Online-Ausgabe 978-1-4757-4101-8 Graduate texts in mathematics. 49 (DE-604)BV000000067 49 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001474865&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 | Gruenberg, Karl W. 1928-2007 Weir, Alan J. Linear geometry Graduate texts in mathematics. Algèbre linéaire Géométrie algébrique Lineaire algebra gtt Meetkunde gtt Algebras, Linear Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd Lineare Geometrie (DE-588)4181966-4 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4181966-4 (DE-588)4035811-2 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Linear geometry |
| title_auth | Linear geometry |
| title_exact_search | Linear geometry |
| title_full | Linear geometry K. W. Gruenberg ; A. J. Weir |
| title_fullStr | Linear geometry K. W. Gruenberg ; A. J. Weir |
| title_full_unstemmed | Linear geometry K. W. Gruenberg ; A. J. Weir |
| title_short | Linear geometry |
| title_sort | linear geometry |
| topic | Algèbre linéaire Géométrie algébrique Lineaire algebra gtt Meetkunde gtt Algebras, Linear Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd Lineare Geometrie (DE-588)4181966-4 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Géométrie algébrique Lineaire algebra Meetkunde Algebras, Linear Geometry, Algebraic Algebraische Geometrie Lineare Geometrie Lineare Algebra Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001474865&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT gruenbergkarlw lineargeometry AT weiralanj lineargeometry |