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Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

2016-04-19 Computers
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Release : 2016-04-19
Genre : Computers
Kind : eBook
Book Rating : 393/5 ( reviews)

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Book Synopsis Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs by : Jason J. Molitierno

Download or read book Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs written by Jason J. Molitierno. This book was released on 2016-04-19. Available in PDF, EPUB and Kindle. Book excerpt: 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

Combinatorial Matrix Theory

2018-03-31 Mathematics
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Release : 2018-03-31
Genre : Mathematics
Kind : eBook
Book Rating : 534/5 ( reviews)

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Book Synopsis Combinatorial Matrix Theory by : Richard A. Brualdi

Download or read book Combinatorial Matrix Theory written by Richard A. Brualdi. This book was released on 2018-03-31. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Generalized Inverses of Matrices

2013-02-11 Mathematics
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Release : 2013-02-11
Genre : Mathematics
Kind : eBook
Book Rating : 530/5 ( reviews)

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Book Synopsis Combinatorial Matrix Theory and Generalized Inverses of Matrices by : Ravindra B. Bapat

Download or read book Combinatorial Matrix Theory and Generalized Inverses of Matrices written by Ravindra B. Bapat. This book was released on 2013-02-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrices in Combinatorics and Graph Theory

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 655/5 ( reviews)

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Book Synopsis Matrices in Combinatorics and Graph Theory by : Bolian Liu

Download or read book Matrices in Combinatorics and Graph Theory written by Bolian Liu. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Combinatorial Approach to Matrix Theory and Its Applications

2008-08-06 Mathematics
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Release : 2008-08-06
Genre : Mathematics
Kind : eBook
Book Rating : 241/5 ( reviews)

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Book Synopsis A Combinatorial Approach to Matrix Theory and Its Applications by : Richard A. Brualdi

Download or read book A Combinatorial Approach to Matrix Theory and Its Applications written by Richard A. Brualdi. This book was released on 2008-08-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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