Eigenvalues, multiplicities and graphs:
The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified de...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2018
|
| Series: | Cambridge tracts in mathematics
211 |
| Subjects: | |
| Online Access: | BSB01 FHN01 TUM01 TUM02 UBA01 UBR01 Volltext |
| Summary: | The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject |
| Physical Description: | 1 Online-Ressource (xxii, 291 Seiten) |
| ISBN: | 9781316155158 |
| DOI: | 10.1017/9781316155158 |
Staff View
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:04:55Z |
| institution | BVB |
| isbn | 9781316155158 |
| language | English |
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| physical | 1 Online-Ressource (xxii, 291 Seiten) |
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| spelling | Johnson, Charles R. 1948- Verfasser (DE-588)143876384 aut Eigenvalues, multiplicities and graphs Charles R. Johnson, Carlos M. Saiago Cambridge Cambridge University Press 2018 1 Online-Ressource (xxii, 291 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 211 The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject Eigenvalues Matrices Symmetric matrices Trees (Graph theory) Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf Eigenwertverteilung (DE-588)4123087-5 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s Eigenwert (DE-588)4151200-5 s Eigenwertverteilung (DE-588)4123087-5 s DE-604 Saiago, Carlos M. Verfasser (DE-588)1156043670 aut Erscheint auch als Druck-Ausgabe, hardback 978-1-107-09545-8 Cambridge tracts in mathematics 211 (DE-604)BV047362617 211 https://doi.org/10.1017/9781316155158 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Johnson, Charles R. 1948- Saiago, Carlos M. Eigenvalues, multiplicities and graphs Cambridge tracts in mathematics Eigenvalues Matrices Symmetric matrices Trees (Graph theory) Matrix Mathematik (DE-588)4037968-1 gnd Eigenwert (DE-588)4151200-5 gnd Eigenwertverteilung (DE-588)4123087-5 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4151200-5 (DE-588)4123087-5 |
| title | Eigenvalues, multiplicities and graphs |
| title_auth | Eigenvalues, multiplicities and graphs |
| title_exact_search | Eigenvalues, multiplicities and graphs |
| title_full | Eigenvalues, multiplicities and graphs Charles R. Johnson, Carlos M. Saiago |
| title_fullStr | Eigenvalues, multiplicities and graphs Charles R. Johnson, Carlos M. Saiago |
| title_full_unstemmed | Eigenvalues, multiplicities and graphs Charles R. Johnson, Carlos M. Saiago |
| title_short | Eigenvalues, multiplicities and graphs |
| title_sort | eigenvalues multiplicities and graphs |
| topic | Eigenvalues Matrices Symmetric matrices Trees (Graph theory) Matrix Mathematik (DE-588)4037968-1 gnd Eigenwert (DE-588)4151200-5 gnd Eigenwertverteilung (DE-588)4123087-5 gnd |
| topic_facet | Eigenvalues Matrices Symmetric matrices Trees (Graph theory) Matrix Mathematik Eigenwert Eigenwertverteilung |
| url | https://doi.org/10.1017/9781316155158 |
| volume_link | (DE-604)BV047362617 |
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