A combinatorial approach to matrix theory and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2009
|
| Schriftenreihe: | Discrete mathematics and its applications
52 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIII, 267 S. Ill. |
| ISBN: | 9781420082234 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV035043425 | ||
| 003 | DE-604 | ||
| 005 | 20111128 | ||
| 007 | t | ||
| 008 | 080908s2009 xxua||| |||| 00||| eng d | ||
| 010 | |a 2008014627 | ||
| 020 | |a 9781420082234 |c hardback : alk. paper |9 978-1-4200-8223-4 | ||
| 035 | |a (OCoLC)220099985 | ||
| 035 | |a (DE-599)BVBBV035043425 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-20 |a DE-703 |a DE-29T |a DE-11 |a DE-83 |a DE-91G | ||
| 050 | 0 | |a QA188 | |
| 082 | 0 | |a 512.9/434 | |
| 084 | |a SK 220 |0 (DE-625)143224: |2 rvk | ||
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a 15-01 |2 msc | ||
| 084 | |a MAT 050f |2 stub | ||
| 084 | |a 05C50 |2 msc | ||
| 084 | |a MAT 150f |2 stub | ||
| 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 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016712215 | ||
Datensatz im Suchindex
| _version_ | 1804137979338293248 |
|---|---|
| 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
|
| adam_txt |
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 |
| any_adam_object_boolean | 1 |
| author | Brualdi, Richard A. 1939- |
| author_GND | (DE-588)113645112 (DE-588)110230485 |
| author_facet | Brualdi, Richard A. 1939- |
| author_role | aut |
| author_sort | Brualdi, Richard A. 1939- |
| author_variant | r a b ra rab |
| building | Verbundindex |
| bvnumber | BV035043425 |
| callnumber-first | Q - Science |
| callnumber-label | QA188 |
| callnumber-raw | QA188 |
| callnumber-search | QA188 |
| callnumber-sort | QA 3188 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 SK 890 |
| 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 |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02056nam a2200517zcb4500</leader><controlfield tag="001">BV035043425</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20111128 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080908s2009 xxua||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2008014627</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781420082234</subfield><subfield code="c">hardback : alk. paper</subfield><subfield code="9">978-1-4200-8223-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)220099985</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035043425</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-91G</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.9/434</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 220</subfield><subfield code="0">(DE-625)143224:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">15-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 050f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">05C50</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 150f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Brualdi, Richard A.</subfield><subfield code="d">1939-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)113645112</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A combinatorial approach to matrix theory and its applications</subfield><subfield code="c">Richard A. Brualdi ; Dragoš Cvetković</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton [u.a.]</subfield><subfield code="b">CRC Press</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 267 S.</subfield><subfield code="b">Ill.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Discrete mathematics and its applications</subfield><subfield code="v">52</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrices</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Combinatorial analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorische Analysis</subfield><subfield code="0">(DE-588)4164746-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Matrix</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4037968-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Matrix</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4037968-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Kombinatorische Analysis</subfield><subfield code="0">(DE-588)4164746-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Cvetković, Dragoš M.</subfield><subfield code="d">1941-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)110230485</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Discrete mathematics and its applications</subfield><subfield code="v">52</subfield><subfield code="w">(DE-604)BV023551867</subfield><subfield code="9">52</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016712215</subfield></datafield></record></collection> |
| id | DE-604.BV035043425 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:53:57Z |
| indexdate | 2024-07-09T21:20:54Z |
| institution | BVB |
| isbn | 9781420082234 |
| language | English |
| lccn | 2008014627 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016712215 |
| oclc_num | 220099985 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-29T DE-11 DE-83 DE-91G DE-BY-TUM |
| 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 |
| spelling | Brualdi, Richard A. 1939- Verfasser (DE-588)113645112 aut A combinatorial approach to matrix theory and its applications Richard A. Brualdi ; Dragoš Cvetković Boca Raton [u.a.] CRC Press 2009 XIII, 267 S. Ill. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications 52 Includes bibliographical references and index Matrices Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s Kombinatorische Analysis (DE-588)4164746-4 s DE-604 Cvetković, Dragoš M. 1941- Sonstige (DE-588)110230485 oth Discrete mathematics and its applications 52 (DE-604)BV023551867 52 Digitalisierung UB Bayreuth application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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 |