Cargando…
Eigenvalues, multiplicities and graphs /
This book investigates the influence of the graph of a symmetric matrix on the multiplicities of its eigenvalues.
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, United Kingdom :
Cambridge University Press,
2018.
|
| Colección: | Cambridge tracts in mathematics ;
211. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | EBSCO_on1025334932 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr mn||||||||| | ||
| 008 | 180227t20182018enka ob 001 0 eng d | ||
| 040 | |a IQU |b eng |e rda |e pn |c IQU |d IQU |d N$T |d OCLCA |d N$T |d EBLCP |d MERER |d YDX |d OCLCF |d OCLCQ |d OSU |d U3W |d INT |d OTZ |d AU@ |d OCLCQ |d OCL |d OCLCQ |d UKAHL |d OCLCQ |d OCLCO |d OCLCQ |d S9M | ||
| 019 | |a 1026492231 |a 1028851343 |a 1029207056 |a 1029273739 |a 1029304886 |a 1030562059 |a 1043768507 |a 1044829426 |a 1117250878 |a 1118511517 |a 1167428931 | ||
| 020 | |a 9781108548137 |q (electronic bk.) | ||
| 020 | |a 110854813X |q (electronic bk.) | ||
| 020 | |z 9781107095458 |q (hardback) | ||
| 020 | |z 110709545X |q (hardback) | ||
| 020 | |z 9781316155158 | ||
| 020 | |z 1316155153 | ||
| 029 | 1 | |a AU@ |b 000062230260 | |
| 029 | 1 | |a AU@ |b 000062883319 | |
| 035 | |a (OCoLC)1025334932 |z (OCoLC)1026492231 |z (OCoLC)1028851343 |z (OCoLC)1029207056 |z (OCoLC)1029273739 |z (OCoLC)1029304886 |z (OCoLC)1030562059 |z (OCoLC)1043768507 |z (OCoLC)1044829426 |z (OCoLC)1117250878 |z (OCoLC)1118511517 |z (OCoLC)1167428931 | ||
| 050 | 4 | |a QA193 |b .J64 2018eb | |
| 072 | 7 | |a MAT |x 002040 |2 bisacsh | |
| 082 | 0 | 4 | |a 512.9/434 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Johnson, Charles R., |e author. | |
| 245 | 1 | 0 | |a Eigenvalues, multiplicities and graphs / |c Charles R. Johnson, College of William and Mary, Williamsburg, Virginia ; Carlos M. Saiago, Universidade Nova de Lisboa. |
| 264 | 1 | |a Cambridge, United Kingdom : |b Cambridge University Press, |c 2018. | |
| 264 | 4 | |c ©2018 | |
| 300 | |a 1 online resource (xxii, 291 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics ; |v 211 | |
| 520 | |a This book investigates the influence of the graph of a symmetric matrix on the multiplicities of its eigenvalues. | ||
| 504 | |a Includes bibliographical references (pages 281-286) and index. | ||
| 505 | 0 | 0 | |g Background -- |g Introduction -- |t Parter-Wiener, etc. theory -- |t Maximum multiplicity for trees, I -- |t Multiple eigenvalues and structure -- |t Maximum multiplicity, II -- |t The minimum number of distinct eigenvalues -- |t Construction techniques -- |t Multiplicity lists for generalized stars -- |t Double generalized stars -- Linear trees -- |t Nontrees -- |t Geometric multiplicities for general matrices over a field. |
| 505 | 0 | 0 | |g Maximum Multiplicity for Trees, I -- |g 3.1. |t Introduction -- |g 3.2. |t Path Covers and Path Trees -- |g 3.3. |t [delta](T) = Maximum p-q -- |g 3.4. |t M(T) = P(T), [delta](T), n -- mr(T) -- |g 3.5. |t Calculation of M(T) and Bounds -- |g 3.5.1. |t Calculation of M(T) in Linear Time -- |g 3.5.2. |t Estimation of M(T) from the Degree Sequence of T -- |g 4. |t Multiple Eigenvalues and Structure -- |g 4.1. |t Perturbation of Diagonal Entries and Vertex Status -- |g 4.2. |t Parter Vertices, Parter Sets and Fragmentation -- |g 4.3. |t Fundamental Decomposition -- |g 4.4. |t Eigenspace Structure and Vertex Classification -- |g 4.5. |t Removal of an Edge -- |g 4.5.1. |t Basic Inequalities -- |g 4.5.2. |t Classification of Edges in Trees Based on the Classification of Their Vertices -- |g 5. |t Maximum Multiplicity, II -- |g 5.1. |t Structure of Matrices with a Maximum Multiplicity Eigenvalue -- |g 5.2. |t NIM Trees -- |g 5.3. |t Second Maximum Multiplicity -- |g 6. |t Minimum Number of Distinct Eigenvalues -- |g 6.1. |t Introduction -- |g 6.2. |t Diameter and a Lower Bound for c(T) -- |g 6.3. |t Method of Branch Duplication: Combinatorial and Algebraic -- |g 6.4. |t Converse to the Diameter Lower Bound for Trees -- |g 6.5. |t Trees of Diameter 7 -- |g 6.6. |t Function C(d) and Disparity -- |g 6.7. |t Minimum Number of Multiplicities Equal to 1 -- |g 6.8. |t Relative Position of Multiple Eigenvalues in Ordered Lists -- |g 6.8.1. |t Lower Bound for the Cardinality of a Fragmenting Parter Set -- |g 6.8.2. |t Relative Position of a Single Multiple Eigenvalue -- |g 6.8.3. |t Vertex Degrees -- |g 6.8.4. |t Two Multiple Eigenvalues -- |g 7. |t Construction Techniques -- |g 7.1. |t Introduction -- |g 7.2. |t Eigenvalues for Paths and Subpaths -- |g 7.3. |t Method of Assignments -- |g 7.4. |t Derivation of a Multiplicity List via Assignment: An Example -- |g 7.5. |t 13-Vertex Example -- |g 7.6. |t Implicit Function Theorem (IFT) Approach -- |g 7.7. |t More IFT, Examples, Vines -- |g 7.8. |t Polynomial Constructions -- |g 8. |t Multiplicity Lists for Generalized Stars -- |g 8.1. |t Introduction -- |g 8.2. |t Characterization of Generalized Stars -- |g 8.3. |t Case of Simple Stars -- |g 8.4. |t Inverse Eigenvalue Problem for Generalized Stars -- |g 8.5. |t Multiplicity Lists -- |g 8.6. |t IEP versus Ordered Multiplicity Lists -- |g 8.7. |t Upward Multiplicity Lists -- |g 8.8. |t c(T) and U(T) -- |g 9. |t Double Generalized Stars -- |g 9.1. |t Introduction -- |g 9.2. |t Observations about Double Generalized Stars -- |g 9.3. |t Multiplicity Lists -- |g 9.4. |t Double Paths -- |g 10. |t Linear Trees -- |g 10.1. |t Introduction -- |g 10.2. |t Second Superposition Principle for Linear Trees -- |g 10.3. |t Possible Multiplicity Lists for Linear Trees -- |g 10.4. |t Cases of Sufficiency of Linear Trees -- |g 10.5. |t Special Results for Linear Trees -- |g 11. |t Nontrees -- |g 11.1. |t Introduction and Observations -- |g 11.2. |t Complete Graph -- |g 11.3. |t Cycle -- |g 11.4. |t Tree + an Edge -- |g 11.4.1. |t Graph + an Edge -- |g 11.5. |t Graphs G for Which M(G) = 2 -- |g 11.6. |t Graphs Permitting Just Two Distinct Eigenvalues -- |g 11.7. |t Nearly Complete Graphs -- |g 12. |t Geometric Multiplicities for General Matrices over a Field -- |g 12.1. |t Preliminaries -- |g 12.2. |t Geometric Parter-Wiener, etc. Theory -- |g 12.3. |t Geometric Downer Branch Mechanism for General Matrices over a Field -- |g 12.4. |t Maximum Geometric Multiplicity for a Tree -- |g 12.5. |t Minimum Number of Distinct Eigenvalues in a Diagonalizable Matrix Whose Graph Is a Tree -- |g Appendix |t A Multiplicity Lists for Trees on Fewer Than 12 Vertices -- |g A.1. |t Tree on 3 Vertices (1 tree) -- |g A.2. |t Trees on 4 Vertices (2 trees) -- |g A.3. |t Trees on 5 Vertices (3 trees) -- |g A.4. |t Trees. |
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Eigenvalues. | |
| 650 | 0 | |a Matrices. | |
| 650 | 0 | |a Symmetric matrices. | |
| 650 | 0 | |a Trees (Graph theory) | |
| 650 | 6 | |a Valeurs propres. | |
| 650 | 6 | |a Matrices. | |
| 650 | 6 | |a Matrices symétriques. | |
| 650 | 6 | |a Arbres (Théorie des graphes) | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Teoría de grafos |2 embne | |
| 650 | 7 | |a Matrices (Matemáticas) |2 embne | |
| 650 | 7 | |a Eigenvalues |2 fast | |
| 650 | 7 | |a Matrices |2 fast | |
| 650 | 7 | |a Symmetric matrices |2 fast | |
| 650 | 7 | |a Trees (Graph theory) |2 fast | |
| 700 | 1 | |a Saiago, Carlos M., |e author. | |
| 776 | 0 | 8 | |i Print version: |a Johnson, Charles R. |t Eigenvalues, multiplicities and graphs. |d Cambridge, United Kingdom : Cambridge University Press, 2018 |z 110709545X |w (OCoLC)991790102 |
| 830 | 0 | |a Cambridge tracts in mathematics ; |v 211. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1694366 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH34209553 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL5312925 | ||
| 938 | |a EBSCOhost |b EBSC |n 1694366 | ||
| 938 | |a YBP Library Services |b YANK |n 15158250 | ||
| 994 | |a 92 |b IZTAP | ||