Combinatorial Matrix Classes

Author : Richard A. Brualdi
Publisher : Cambridge University Press
ISBN 13 : 0521865654
Total Pages : 26 pages
Book Rating : 4.54/5 ( download)

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Download or read book Combinatorial Matrix Classes written by Richard A. Brualdi and published by Cambridge University Press. This book was released on 2006-08-10 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Richard A. Brualdi
Publisher :
ISBN 13 : 9781139883344
Total Pages : 544 pages
Book Rating : 4.48/5 ( download)

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Download or read book Combinatorial Matrix Classes written by Richard A. Brualdi and published by . This book was released on 2006 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough development of certain classes of matrices that have combinatorial definitions or significance.

Author : Richard A. Brualdi
Publisher : Birkhäuser
ISBN 13 : 3319709534
Total Pages : 219 pages
Book Rating : 4.36/5 ( download)

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Download or read book Combinatorial Matrix Theory written by Richard A. Brualdi and published by Birkhäuser. This book was released on 2018-03-31 with total page 219 pages. 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.

Author : Richard A. Brualdi
Publisher :
ISBN 13 : 9781107094000
Total Pages : 380 pages
Book Rating : 4.03/5 ( download)

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Download or read book Combinatorial Matrix Theory written by Richard A. Brualdi and published by . This book was released on 1991 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Richard A. Brualdi
Publisher :
ISBN 13 : 9781107087750
Total Pages : 380 pages
Book Rating : 4.59/5 ( download)

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Download or read book Combinatorial Matrix Theory written by Richard A. Brualdi and published by . This book was released on 2014-05-14 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory.

Author : Charles R. Johnson
Publisher : Cambridge University Press
ISBN 13 : 1108478719
Total Pages : 223 pages
Book Rating : 4.17/5 ( download)

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Download or read book Matrix Positivity written by Charles R. Johnson and published by Cambridge University Press. This book was released on 2020-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.

Author : Stephan Ramon Garcia
Publisher : Cambridge University Press
ISBN 13 : 1107103819
Total Pages : 447 pages
Book Rating : 4.18/5 ( download)

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Download or read book A Second Course in Linear Algebra written by Stephan Ramon Garcia and published by Cambridge University Press. This book was released on 2017-05-11 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.

Author : Dragan Stevanovic
Publisher : Academic Press
ISBN 13 : 0128020970
Total Pages : 167 pages
Book Rating : 4.75/5 ( download)

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Download or read book Spectral Radius of Graphs written by Dragan Stevanovic and published by Academic Press. This book was released on 2014-10-13 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the book delves deeper into the properties of the principal eigenvector; a critical subject as many of the results on the spectral radius of graphs rely on the properties of the principal eigenvector for their proofs. A following chapter surveys spectral radius of special graphs, covering multipartite graphs, non-regular graphs, planar graphs, threshold graphs, and others. Finally, the work explores results on the structure of graphs having extreme spectral radius in classes of graphs defined by fixing the value of a particular, integer-valued graph invariant, such as: the diameter, the radius, the domination number, the matching number, the clique number, the independence number, the chromatic number or the sequence of vertex degrees. Throughout, the text includes the valuable addition of proofs to accompany the majority of presented results. This enables the reader to learn tricks of the trade and easily see if some of the techniques apply to a current research problem, without having to spend time on searching for the original articles. The book also contains a handful of open problems on the topic that might provide initiative for the reader's research. Dedicated coverage to one of the most prominent graph eigenvalues Proofs and open problems included for further study Overview of classical topics such as spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem

Author : Ravindra B. Bapat
Publisher : Springer Science & Business Media
ISBN 13 : 8132210530
Total Pages : 283 pages
Book Rating : 4.35/5 ( download)

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Download or read book Combinatorial Matrix Theory and Generalized Inverses of Matrices written by Ravindra B. Bapat and published by Springer Science & Business Media. This book was released on 2013-02-11 with total page 283 pages. 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.

Author : Jason J. Molitierno
Publisher : CRC Press
ISBN 13 : 1439863393
Total Pages : 425 pages
Book Rating : 4.98/5 ( download)

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Download or read book Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs written by Jason J. Molitierno and published by CRC Press. This book was released on 2016-04-19 with total page 425 pages. 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