Matrices of sign-solvable linear systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1995
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
116 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 298 S. graph. Darst. |
| ISBN: | 9780521105828 9780521482967 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface page xi
1 Sign solvability 1
1.1 A problem in economics 1
1.2 Sign solvable linear systems 4
Bibliography 16
2 ^ matrices 18
2.1 Signings 18
2.2 Indecomposability 22
2.3 L canonical form 31
Bibliography 33
3 Sign solvability and digraphs 35
3.1 Partial sign solvability 35
3.2 Digraph characterizations 42
3.3 Sign solvability and digraphs 53
Bibliography 60
4 S* matrices 62
4.1 ,S * matrices and SNS* matrices 62
4.2 Recursive structure 66
4.3 Zero patterns of 5 matrices 73
4.4 Maximal S matrices 79
Bibliography 85
vii
viii Contents
5 Beyond S* matrices 87
5.1 Totally L matrices 87
5.2 Recursive structure of totally I matrices 90
5.3 Signed compound 95
5.4 Sign central matrices 99
Bibliography 105
6 SNS matrices 106
6.1 Zero patterns of SNS matrices 106
6.2 Maximal SNS matrices 114
6.3 Zero patterns of partly decomposable maximal SNS matrices 134
6.4 SNS matrices and the permanent 138
6.5 Characterizations of zero patterns of SNS matrices 146
6.6 Combinatorially symmetric SNS matrices 157
Bibliography 165
7 S2NS matrices 168
7.1 Fully indecomposable S2NS matrices 168
7.2 Zero patterns of S2NS matrices 178
7.3 Partly decomposable S2NS matrices 185
7.4 S2NS matrices whose inverses are S2NS matrices 191
7.5 Inverses of fully indecomposable S2NS matrices 197
Bibliography 202
8 Extremal properties of // matrices 203
8.1 Maximal SNS matrices 203
8.2 SNS matrices 210
8.3 Barely L matrices 218
Bibliography 223
9 The inverse sign pattern graph 225
9.1 General properties of the inverse sign pattern graph 225
9.2 Inverse positive sign patterns 231
Bibliography 238
10 Sign stability 239
10.1 A problem from ecology 239
10.2 Sign stable matrices 243
10.3 Stably sign solvable linear systems 248
10.4 SNS matrices with other eigenvalue restrictions 254
Bibliography 257
Contents ix
11 Related topics 259
11.1 Conditional sign solvability 259
11.2 Least squares sign solvability 265
11.3 Variation of rank over a qualitative class 275
11.4 SkewSNS matrices and pfaffians 277
11.5 SNS matrix pairs 281
11.6 Nonsingular strength of a matrix 284
Bibliography 287
Master bibliography 289
Index 295
|
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| id | DE-604.BV010644973 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:31Z |
| institution | BVB |
| isbn | 9780521105828 9780521482967 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007103080 |
| oclc_num | 439798213 |
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| physical | XII, 298 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Brualdi, Richard A. 1939- Verfasser (DE-588)113645112 aut Matrices of sign-solvable linear systems Richard A. Brualdi ; Bryan L. Shader Matrices of sign solvable linear systems 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1995 XII, 298 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 116 Algebra - Linearna algebra - Kombinatorika Vorzeichen Mathematik (DE-588)4503227-0 gnd rswk-swf Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Matrizentheorie (DE-588)4128970-5 s Kombinatorik (DE-588)4031824-2 s DE-604 Vorzeichen Mathematik (DE-588)4503227-0 s Shader, Bryan L. Verfasser (DE-588)142400866 aut Erscheint auch als Online-Ausgabe 978-0-511-57473-3 Cambridge tracts in mathematics 116 (DE-604)BV000000001 116 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007103080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brualdi, Richard A. 1939- Shader, Bryan L. Matrices of sign-solvable linear systems Cambridge tracts in mathematics Algebra - Linearna algebra - Kombinatorika Vorzeichen Mathematik (DE-588)4503227-0 gnd Matrizentheorie (DE-588)4128970-5 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4503227-0 (DE-588)4128970-5 (DE-588)4031824-2 |
| title | Matrices of sign-solvable linear systems |
| title_alt | Matrices of sign solvable linear systems |
| title_auth | Matrices of sign-solvable linear systems |
| title_exact_search | Matrices of sign-solvable linear systems |
| title_full | Matrices of sign-solvable linear systems Richard A. Brualdi ; Bryan L. Shader |
| title_fullStr | Matrices of sign-solvable linear systems Richard A. Brualdi ; Bryan L. Shader |
| title_full_unstemmed | Matrices of sign-solvable linear systems Richard A. Brualdi ; Bryan L. Shader |
| title_short | Matrices of sign-solvable linear systems |
| title_sort | matrices of sign solvable linear systems |
| topic | Algebra - Linearna algebra - Kombinatorika Vorzeichen Mathematik (DE-588)4503227-0 gnd Matrizentheorie (DE-588)4128970-5 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Algebra - Linearna algebra - Kombinatorika Vorzeichen Mathematik Matrizentheorie Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007103080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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