A combinatorial approach to matrix theory and its applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2009
|
| Schriftenreihe: | Discrete mathematics and its applications
52 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016712215&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references and index |
| Umfang: | XIII, 267 S. Ill. |
| ISBN: | 9781420082234 |
Internformat
MARC
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| 100 | 1 | |a Brualdi, Richard A. |d 1939- |e Verfasser |0 (DE-588)113645112 |4 aut | |
| 245 | 1 | 0 | |a A combinatorial approach to matrix theory and its applications |c Richard A. Brualdi ; Dragoš Cvetković |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2009 | |
| 300 | |a XIII, 267 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Discrete mathematics and its applications |v 52 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 0 | 7 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Matrix |g Mathematik |0 (DE-588)4037968-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Matrix |g Mathematik |0 (DE-588)4037968-1 |D s |
| 689 | 0 | 1 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Cvetković, Dragoš M. |d 1941- |e Sonstige |0 (DE-588)110230485 |4 oth | |
| 830 | 0 | |a Discrete mathematics and its applications |v 52 |w (DE-604)BV023551867 |9 52 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016712215 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0040 MAT 150f 2011 A 8025 0102 MAT 150f 2011 A 8025 |
|---|---|
| DE-BY-TUM_katkey | 1803580 |
| DE-BY-TUM_location | LSB 01 |
| DE-BY-TUM_media_number | 040071287604 040071411195 |
| _version_ | 1821933635566043136 |
| adam_text | Contents
Preface
xi
Dedication
xv
1
Introduction
1
1.1
Graphs
......................... 2
1.2
Digraphs
......................... 8
1.3
Some Classical Combinatorics
............ 10
1.4
Fields
......................... 13
1.5
Vector Spaces
..................... 17
1.6
Exercises
........................ 23
2
Basic Matrix Operations
27
2.1
Basic Concepts
.................... 27
2.2
The
König
Digraph of a Matrix
........... 35
2.3
Partitioned Matrices
................. 43
2.4
Exercises
........................ 46
3
Powers of Matrices
49
3.1
Matrix Powers and Digraphs
............. 49
3.2
Circulant
Matrices
.................. 58
3.3
Permutations with Restrictions
........... 59
3.4
Exercises
........................ 60
4
Determinants
63
4.1
Definition of the Determinant
............ 63
4.2
Properties of Determinants
.............. 72
4.3
A Special Determinant Formula
........... 85
vn
viii CONTENTS
4.4
Classical Definition of the Determinant
....... 87
4.5
Laplace Determinant Development
......... 91
4.6
Exercises
........................ 94
5
Matrix Inverses
97
5.1
Adjoint and Its Determinant
............. 97
5.2
Inverse of a Square Matrix
.............. 101
5.3
Graph-Theoretic Interpretation
........... 103
5.4
Exercises
........................ 107
6
Systems of Linear Equations
109
6.1
Solutions of Linear Systems
............. 109
6.2
Cramer s Formula
................... 118
6.3
Solving Linear Systems by Digraphs
......... 121
6.4
Signal Flow Digraphs of Linear Systems
...... 127
6.5
Sparse Matrices
.................... 133
6.6
Exercises
........................ 137
7
Spectrum of a Matrix
139
7.1
Eigenvectors and Eigenvalues
............ 139
7.2
The Cayley-Hamilton Theorem
........... 147
7.3
Similar Matrices and the JCF
............ 150
7.4
Spectrum of
Circulants
................ 165
7.5
Exercises
........................ 167
8
Nonnegative
Matrices
171
8.1
Irreducible and Reducible Matrices
......... 171
8.2
Primitive and
Imprimitive
Matrices
......... 174
8.3
The Perron-Frobenius Theorem
........... 179
8.4
Graph Spectra
..................... 184
8.5
Exercises
........................ 188
9
Additional Topics
191
9.1
Tensor and
Hadamard
Product
........... 191
9.2
Eigenvalue Inclusion Regions
............. 196
9.3
Permanent and SNS-Matrices
............ 204
9.4
Exercises
........................ 215
CONTENTS ix
10 Applications 217
10.1
Electrical
Engineering:
Flow Graphs
........218
10.2
Physics: Vibration of a Membrane
..........224
10.3
Chemistry: Unsaturated Hydrocarbons
.......229
10.4
Exercises
........................240
Coda
241
Answers and Hints
245
Bibliography
253
Index
261
|
| any_adam_object | 1 |
| author | Brualdi, Richard A. 1939- |
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| classification_tum | MAT 050f MAT 150f |
| ctrlnum | (OCoLC)220099985 (DE-599)BVBBV035043425 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035043425 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:18:45Z |
| institution | BVB |
| isbn | 9781420082234 |
| language | English |
| lccn | 2008014627 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016712215 |
| oclc_num | 220099985 |
| open_access_boolean | |
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| owner_facet | DE-20 DE-703 DE-29T DE-11 DE-83 DE-91G DE-BY-TUM |
| physical | XIII, 267 S. Ill. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | CRC Press |
| record_format | marc |
| series | Discrete mathematics and its applications |
| series2 | Discrete mathematics and its applications |
| spellingShingle | Brualdi, Richard A. 1939- A combinatorial approach to matrix theory and its applications Discrete mathematics and its applications Matrices Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4164746-4 (DE-588)4037968-1 |
| title | A combinatorial approach to matrix theory and its applications |
| title_auth | A combinatorial approach to matrix theory and its applications |
| title_exact_search | A combinatorial approach to matrix theory and its applications |
| title_full | A combinatorial approach to matrix theory and its applications Richard A. Brualdi ; Dragoš Cvetković |
| title_fullStr | A combinatorial approach to matrix theory and its applications Richard A. Brualdi ; Dragoš Cvetković |
| title_full_unstemmed | A combinatorial approach to matrix theory and its applications Richard A. Brualdi ; Dragoš Cvetković |
| title_short | A combinatorial approach to matrix theory and its applications |
| title_sort | a combinatorial approach to matrix theory and its applications |
| topic | Matrices Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Matrices Combinatorial analysis Kombinatorische Analysis Matrix Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016712215&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023551867 |
| work_keys_str_mv | AT brualdiricharda acombinatorialapproachtomatrixtheoryanditsapplications AT cvetkovicdragosm acombinatorialapproachtomatrixtheoryanditsapplications |
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| Signatur: |
0040 MAT 150f 2011 A 8025
Lageplan |
|---|---|
| Exemplar 1 | Dauerhaft ausgeliehen Ausgeliehen – Rückgabe bis: 31.12.9999 |
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 150f 2011 A 8025
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |