Linear algebra and geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XXI, 526 S. Ill., graph. Darst. |
| ISBN: | 9783642309939 |
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MARC
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| 240 | 1 | 0 | |a Linejnaja algebra i geometrija |
| 245 | 1 | 0 | |a Linear algebra and geometry |c Igor R. Shafarevich ; Alexey O. Remizov |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XXI, 526 S. |b Ill., graph. Darst. | ||
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| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrie |0 (DE-588)4020236-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1 LINEAR EQUATIONS 1
1.1 LINEAR EQUATIONS AND FUNCTIONS 1
1.2 GAUSSIAN ELIMINATION 6
1.3 EXAMPLES* 15
2 MATRICES AND DETERMINANTS 25
2.1 DETERMINANTS O F ORDERS 2 AND 3 25
2.2 DETERMINANTS OF ARBITRARY ORDER 30
2.3 PROPERTIES THAT CHARACTERIZE DETERMINANTS 37
2.4 EXPANSION OF A DETERMINANT ALONG ITS COLUMNS 39
2.5 CRAMER'S RULE 4 2
2.6 PERMUTATIONS, SYMMETRIC AND ANTISYMMETRIC FUNCTIONS 44
2.7 EXPLICIT FORMULA FOR THE DETERMINANT 5 0
2.8 THE RANK OF A MATRIX 53
2.9 OPERATIONS ON MATRICES 6 0
2.10 INVERSE MATRICES 70
3 VECTOR SPACES 79
3.1 THE DEFINITION O F A VECTOR SPACE 79
3.2 DIMENSION AND BASIS 86
3.3 LINEAR TRANSFORMATIONS O F VECTOR SPACES 101
3.4 CHANGE OF COORDINATES 107
3.5 ISOMORPHISMS OF VECTOR SPACES 112
3.6 THE RANK OF A LINEAR TRANSFORMATION 118
3.7 DUAL SPACES 120
3.8 FORMS AND POLYNOMIALS IN VECTORS 127
4 LINEAR TRANSFORMATIONS O F A VECTOR SPACE TO ITSELF 133
4.1 EIGENVECTORS AND INVARIANT SUBSPACES 133
4.2 COMPLEX AND REAL VECTOR SPACES 142
4.3 COMPLEXIFICATION 149
4.4 ORIENTATION O F A REAL VECTOR SPACE 154
V I I
HTTP://D-NB.INFO/1022399799
IMAGE 2
VIII CONTENTS
5 JORDAN NORMAL FORM 161
5.1 PRINCIPAL VECTORS AND CYCLIC SUBSPACES 161
5.2 JORDAN NORMAL FORM (DECOMPOSITION) 165
5.3 JORDAN NORMAL FORM (UNIQUENESS) 169
5.4 REAL VECTOR SPACES 173
5.5 APPLICATIONS* 176
6 QUADRATIC AND BILINEAR FORMS 191
6.1 BASIC DEFINITIONS 191
6.2 REDUCTION TO CANONICAL FORM 198
6.3 COMPLEX, REAL, AND HERMITIAN FORMS 204
7 EUCLIDEAN SPACES 213
7.1 THE DEFINITION OF A EUCLIDEAN SPACE 213
7.2 ORTHOGONAL TRANSFORMATIONS 223
7.3 ORIENTATION OF A EUCLIDEAN SPACE* 230
7.4 EXAMPLES* 233
7.5 SYMMETRIC TRANSFORMATIONS 245
7.6 APPLICATIONS TO MECHANICS AND GEOMETRY* 255
7.7 PSEUDO-EUCLIDEAN SPACES 265
7.8 LORENTZ TRANSFORMATIONS 275
8 AFFINE SPACES 289
8.1 THE DEFINITION OF AN AFFINE SPACE 289
8.2 AFFINE SPACES 294
8.3 AFFINE TRANSFORMATIONS 301
8.4 AFFINE EUCLIDEAN SPACES AND MOTIONS 309
9 PROJECTIVE SPACES 319
9.1 DEFINITION O F A PROJECTIVE SPACE 319
9.2 PROJECTIVE TRANSFORMATIONS 328
9.3 THE CROSS RATIO 335
9.4 TOPOLOGICAL PROPERTIES O F PROJECTIVE SPACES* 339
10 THE EXTERIOR PRODUCT AND EXTERIOR ALGEBRAS 349
10.1 PLIICKER COORDINATES OF A SUBSPACE 349
10.2 THE PLIICKER RELATIONS AND THE GRASSMANNIAN 353
10.3 THE EXTERIOR PRODUCT 358
10.4 EXTERIOR ALGEBRAS* 367
10.5 APPENDIX* 374
11 QUADRICS 385
11.1 QUADRICS IN PROJECTIVE SPACE 385
11.2 QUADRICS IN COMPLEX PROJECTIVE SPACE 394
11.3 ISOTROPIC SUBSPACES 398
11.4 QUADRICS IN A REAL PROJECTIVE SPACE 410
11.5 QUADRICS IN A REAL AFFINE SPACE 414
11.6 QUADRICS IN AN AFFINE EUCLIDEAN SPACE 425
11.7 QUADRICS IN THE REAL PLANE* 428
IMAGE 3
CONTENTS I X
12 HYPERBOLIC GEOMETRY 433
12.1 HYPERBOLIC SPACE* 434
12.2 THE AXIOMS OF PLANE GEOMETRY* 443
12.3 SOME FORMULAS OF HYPERBOLIC GEOMETRY* 454
13 GROUPS, RINGS, AND MODULES 467
13.1 GROUPS AND HOMOMORPHISMS 467
13.2 DECOMPOSITION OF FINITE ABELIAN GROUPS 475
13.3 THE UNIQUENESS O F THE DECOMPOSITION 481
13.4 FINITELY GENERATED TORSION MODULES OVER A EUCLIDEAN RING* . . . .
484
14 ELEMENTS O F REPRESENTATION THEORY 497
14.1 BASIC CONCEPTS OF REPRESENTATION THEORY 497
14.2 REPRESENTATIONS OF FINITE GROUPS 503
14.3 IRREDUCIBLE REPRESENTATIONS 508
14.4 REPRESENTATIONS OF ABELIAN GROUPS 511
HISTORICAL NOTE 515
REFERENCES 517
INDEX 521 |
| any_adam_object | 1 |
| author | Šafarevič, Igorʹ R. 1923-2017 Remizov, Aleksej O. 1973- |
| author_GND | (DE-588)119280337 (DE-588)1034372890 |
| author_facet | Šafarevič, Igorʹ R. 1923-2017 Remizov, Aleksej O. 1973- |
| author_role | aut aut |
| author_sort | Šafarevič, Igorʹ R. 1923-2017 |
| author_variant | i r š ir irš a o r ao aor |
| building | Verbundindex |
| bvnumber | BV040450684 |
| classification_rvk | SK 220 SK 380 |
| ctrlnum | (OCoLC)818697798 (DE-599)DNB1022399799 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-09-06T00:24:20Z |
| institution | BVB |
| isbn | 9783642309939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025298345 |
| oclc_num | 818697798 |
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| physical | XXI, 526 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| spelling | Šafarevič, Igorʹ R. 1923-2017 Verfasser (DE-588)119280337 aut Linejnaja algebra i geometrija Linear algebra and geometry Igor R. Shafarevich ; Alexey O. Remizov Berlin [u.a.] Springer 2013 XXI, 526 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Russ. übers. Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Geometrie (DE-588)4020236-7 s DE-604 Remizov, Aleksej O. 1973- Verfasser (DE-588)1034372890 aut Erscheint auch als Online-Ausgabe 978-3-642-30994-6 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4040247&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025298345&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šafarevič, Igorʹ R. 1923-2017 Remizov, Aleksej O. 1973- Linear algebra and geometry Lineare Algebra (DE-588)4035811-2 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4020236-7 |
| title | Linear algebra and geometry |
| title_alt | Linejnaja algebra i geometrija |
| title_auth | Linear algebra and geometry |
| title_exact_search | Linear algebra and geometry |
| title_full | Linear algebra and geometry Igor R. Shafarevich ; Alexey O. Remizov |
| title_fullStr | Linear algebra and geometry Igor R. Shafarevich ; Alexey O. Remizov |
| title_full_unstemmed | Linear algebra and geometry Igor R. Shafarevich ; Alexey O. Remizov |
| title_short | Linear algebra and geometry |
| title_sort | linear algebra and geometry |
| topic | Lineare Algebra (DE-588)4035811-2 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Lineare Algebra Geometrie |
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