Combinatorial Matrix Classes
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Combinatorial Matrix Classes
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Author : Richard A. Brualdi
language : en
Publisher: Cambridge University Press
Release Date : 2006-08-10
Combinatorial Matrix Classes written by Richard A. Brualdi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-10 with Mathematics categories.
A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Several classes of matrices are thoroughly developed including the classes of matrices of 0's and 1's with a specified number of 1's in each row and column (equivalently, bipartite graphs with a specified degree sequence), symmetric matrices in such classes (equivalently, graphs with a specified degree sequence), tournament matrices with a specified number of 1's in each row (equivalently, tournaments with a specified score sequence), nonnegative matrices with specified row and column sums, and doubly stochastic matrices. Most of this material is presented for the first time in book format and the chapter on doubly stochastic matrices provides the most complete development of the topic to date.
Combinatorial Matrix Classes
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Author : Richard A Brualdi
language : en
Publisher:
Release Date : 2014-05-14
Combinatorial Matrix Classes written by Richard A Brualdi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with categories.
A thorough development of certain classes of matrices that have combinatorial definitions or significance.
Combinatorial Matrix Theory
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Author : Richard A. Brualdi
language : en
Publisher: Birkhäuser
Release Date : 2018-03-31
Combinatorial Matrix Theory written by Richard A. Brualdi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-31 with Mathematics categories.
This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.
Combinatorial Matrix Theory
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Author : Richard A. Brualdi
language : en
Publisher:
Release Date : 1991
Combinatorial Matrix Theory written by Richard A. Brualdi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Combinatorial analysis categories.
This is the first book devoted to the exposition of combinatorial matrix theory. It can be used as a graduate course text, but is complete enough for a standard reference work on the basic theory.
Combinatorial Matrix Theory
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Author : Richard A. Brualdi
language : en
Publisher:
Release Date : 2014-05-14
Combinatorial Matrix Theory written by Richard A. Brualdi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory.
Matrices In Combinatorics And Graph Theory
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Author : Bolian Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Matrices In Combinatorics And Graph Theory written by Bolian Liu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given in my book with H. J. Ryser entitled Combinatorial Matrix Theon? where an attempt was made to give a broad picture of the use of combinatorial ideas in matrix theory and the use of matrix theory in proving theorems which, at least on the surface, are combinatorial in nature. In the book by Liu and Lai, this picture is enlarged and expanded to include recent developments and contributions of Chinese mathematicians, many of which have not been readily available to those of us who are unfamiliar with Chinese journals. Necessarily, there is some overlap with the book Combinatorial Matrix Theory. Some of the additional topics include: spectra of graphs, eulerian graph problems, Shannon capacity, generalized inverses of Boolean matrices, matrix rearrangements, and matrix completions. A topic to which many Chinese mathematicians have made substantial contributions is the combinatorial analysis of powers of nonnegative matrices, and a large chapter is devoted to this topic. This book should be a valuable resource for mathematicians working in the area of combinatorial matrix theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press, 1991.
Combinatorial Matrix Theory And Generalized Inverses Of Matrices
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Author : Ravindra B. Bapat
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-11
Combinatorial Matrix Theory And Generalized Inverses Of Matrices written by Ravindra B. Bapat and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-11 with Mathematics categories.
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.
Combinatorics And Random Matrix Theory
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Author : Jinho Baik
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-22
Combinatorics And Random Matrix Theory written by Jinho Baik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-22 with Combinatorial analysis categories.
Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.
A Combinatorial Approach To Matrix Theory And Its Applications
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Author : Richard A. Brualdi
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2008-08-06
A Combinatorial Approach To Matrix Theory And Its Applications written by Richard A. Brualdi and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-06 with Mathematics categories.
Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices. After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.
Applications Of Combinatorial Matrix Theory To Laplacian Matrices Of Graphs
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Author : Jason J. Molitierno
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Applications Of Combinatorial Matrix Theory To Laplacian Matrices Of Graphs written by Jason J. Molitierno and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Computers categories.
On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o