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|a QA193
|b .J64 2018eb
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|a MAT
|x 002040
|2 bisacsh
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|a 512.9/434
|2 23
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|a UAMI
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|a Johnson, Charles R.,
|e author.
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1 |
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|a Eigenvalues, multiplicities and graphs /
|c Charles R. Johnson, College of William and Mary, Williamsburg, Virginia ; Carlos M. Saiago, Universidade Nova de Lisboa.
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264 |
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1 |
|a Cambridge, United Kingdom :
|b Cambridge University Press,
|c 2018.
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264 |
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4 |
|c ©2018
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300 |
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|a 1 online resource (xxii, 291 pages) :
|b illustrations
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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490 |
1 |
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|a Cambridge tracts in mathematics ;
|v 211
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520 |
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|a This book investigates the influence of the graph of a symmetric matrix on the multiplicities of its eigenvalues.
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504 |
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|a Includes bibliographical references (pages 281-286) and index.
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|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.
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505 |
0 |
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|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 |
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|a Print version record.
|
590 |
|
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|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 |
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0 |
|a Trees (Graph theory)
|
650 |
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6 |
|a Valeurs propres.
|
650 |
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6 |
|a Matrices.
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650 |
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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 |
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|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
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