Format:
Online-Ressource (XVII, 277 p. 77 illus., 54 illus. in color, digital)
ISBN:
9788132210535
Series Statement:
SpringerLink
Content:
Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube -- Notes on Explicit Block Diagonalization -- The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs -- Matrix Product of Graphs -- Determinant of the Laplacian Matrix of Weighted Directed Graphs -- From Multivariate Skewed Distributions to Copulas -- Revisiting the BLUE in a Linear Model via Proper Eigenvectors -- Inference in Error Orthogonal Models -- On the Entries of Orthogonal Projection Matrices -- Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces -- The Reverse Order Law in Indefinite Inner Product Spaces -- Generalized Inverses and Approximation Numbers -- On the Level-2 Condition Number for Moore-Penrose Inverse in Hilbert Space -- Products and Sums of Idempotent Matrices over Principal Ideal Domain -- Perfect Semiring of Nonnegative Matrices -- Regular Matrices over an Incline -- Matrix Partial Orders associated with Space Preorder -- An Illustrated Introduction to Some Old Magic Squares from India -- Appendix: Report on CMTGIM 2012, Manipal -- Index.
Content:
This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India.
Note:
"International Workshop and Conference on Combinatorial Matrix Theory and Generalized Inverses of Matrices--2012, was organized by the Department of Statistics, Manipal University Manipal India."--Pref
,
Includes bibliographical references and index
,
Combinatorial Matrix Theory and Generalized Inverses of Matrices; Foreword; Preface; Acknowledgement; Contents; Editors; Contributors; Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube; 1 Introduction; 2 Cartesian Product of Oriented Graphs with Hypercubes; 3 Structured Inverse Eigenvalue Problem (SIEP); 4 Orientation of Hypercubes; 5 The Skew Energy of the Oriented Hypercube Qdphi; References; Notes on Explicit Block Diagonalization; 1 Introduction; 2 Singular Values; 3 q-Analog of EndSn(V(B(n))); 4 Nonbinary Analog of EndSn(V(B(n))); References
,
The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs1 Introduction; 1.1 Immanants of Matrices; 2 The q-Analogue of T's Laplacian; 3 Laplacian of Connected r-Regular Graphs; References; Matrix Product of Graphs; 1 Introduction; 2 Characterization; 3 Further Results; 3.1 Degree of a Vertex in Matrix Product; 3.2 Regular Graphs G for Which A(G)A(G) Is Graphical; References; Determinant of the Laplacian Matrix of a Weighted Directed Graph; 1 Introduction; 2 Determinant of the Laplacian Matrix of a Weighted Directed Graph; References
,
From Multivariate Skewed Distributions to Copulas1 Introduction; 2 Skew-Symmetric Distributions: Notions, Notation, Estimation; 3 Copulas from Skewed Distributions; References; Revisiting the BLUE in a Linear Model via Proper Eigenvectors; 1 Introduction; 2 Preliminaries; 3 When Is PX; W1+y BLUE Under M2?; 4 When Does Every Representation of the BLUE Under M1 Continue to Be BLUE Under M2?; References; Inference in Error Orthogonal Models; 1 Introduction; 2 Homoscedastic Models; 3 EO Models; 4 Mixed Models; 5 An Application; References; On the Entries of Orthogonal Projection Matrices
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1 Preliminaries2 Entries of Orthogonal Projectors; 3 Changes of Entries of Orthogonal Projectors; 4 Linear Regression Model; References; Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces; 1 Introduction and Preliminaries; 2 Moore-Penrose Inverse of Rank-One Perturbed Operators; 3 Formulae for (A+V1GV2*)†; 4 Applications; 4.1 Perturbation Bounds for Nonnegativity of Moore-Penrose Inverses; 4.2 Rank-One Modified Operator and Star Partial Order; References; The Reverse Order Law in Indefinite Inner Product Spaces; 1 Introduction; 2 Notation, Definitions, and Preliminaries
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3 Main ResultsReferences; Generalized Inverses and Approximation Numbers; 1 Introduction; 2 Some Estimates for Approximation Numbers; 3 Closed Range Operators and Approximation Numbers; References; On the Level-2 Condition Number for Moore-Penrose Inverse in Hilbert Space; 1 Introduction; 1.1 Condition Numbers; 1.2 Moore-Penrose Inverse and Its Condition Number; 1.3 Level-2 Condition Numbers; 2 Main Results; 3 Concluding Remark; References; Products and Sums of Idempotent Matrices over Principal Ideal Domains; 1 Introduction; 2 Products of Idempotent Matrices; 3 Sums of Idempotent Matrices
,
References
,
Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube -- Notes on Explicit Block Diagonalization -- The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs -- Matrix Product of Graphs -- Determinant of the Laplacian Matrix of Weighted Directed Graphs -- From Multivariate Skewed Distributions to Copulas -- Revisiting the BLUE in a Linear Model via Proper Eigenvectors -- Inference in Error Orthogonal Models -- On the Entries of Orthogonal Projection Matrices -- Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces -- The Reverse Order Law in Indefinite Inner Product Spaces -- Generalized Inverses and Approximation Numbers -- On the Level-2 Condition Number for Moore-Penrose Inverse in Hilbert Space -- Products and Sums of Idempotent Matrices over Principal Ideal Domain -- Perfect Semiring of Nonnegative Matrices -- Regular Matrices over an Incline -- Matrix Partial Orders associated with Space Preorder -- An Illustrated Introduction to Some Old Magic Squares from India -- Appendix: Report on CMTGIM 2012, Manipal -- Index.
Additional Edition:
ISBN 9788132210528
Additional Edition:
Buchausg. u.d.T. International Workshop on Combinatorial Matrix Theory and Generalized Inverses of Matrices (2012 : Manipal) Combinatorial matrix theory and generalized inverses of matrices New Delhi : Springer, 2013 ISBN 9788132210528
Language:
English
Subjects:
Mathematics
Keywords:
Matrizentheorie
;
Inverse Matrix
;
Konferenzschrift
DOI:
10.1007/978-81-322-1053-5
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
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Author information:
Puntanen, Simo
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