Matrices And Graphs In Geometry

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Matrices And Graphs In Geometry

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Author : Miroslav Fiedler
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-03

Matrices And Graphs In Geometry written by Miroslav Fiedler 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 2011-02-03 with Mathematics categories.

Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.

Graphs And Matrices

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Author : Ravindra B. Bapat
language : en
Publisher: Springer
Release Date : 2014-09-19

Graphs And Matrices written by Ravindra B. Bapat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-19 with Mathematics categories.

This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.

Matrices And Graphs In Geometry

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Author : Miroslav Fiedler
language : en
Publisher:
Release Date : 2014-05-14

Matrices And Graphs In Geometry written by Miroslav Fiedler 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.

Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.

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

Geometry Of Cuts And Metrics

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Author : Michel Marie Deza
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-05-20

Geometry Of Cuts And Metrics written by Michel Marie Deza 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 1997-05-20 with Mathematics categories.

Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.

Graphs And Geometry

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Author : László Lovász
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-28

Graphs And Geometry written by László Lovász 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 2019-08-28 with Mathematics categories.

Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical meaning and applications in proofs and algorithms. This book surveys a number of such connections between graph theory and geometry: among others, rubber band representations, coin representations, orthogonal representations, and discrete analytic functions. Applications are given in information theory, statistical physics, graph algorithms and quantum physics. The book is based on courses and lectures that the author has given over the last few decades and offers readers with some knowledge of graph theory, linear algebra, and probability a thorough introduction to this exciting new area with a large collection of illuminating examples and exercises.

Graphs And Geometry

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Author : László Lovász
language : en
Publisher:
Release Date : 2019

Graphs And Geometry written by László Lovász and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Geometry categories.

Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical meaning and applications in proofs and algorithms. This.

Graph Theory And Sparse Matrix Computation

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Author : Alan George
language : en
Publisher: Springer
Release Date : 2011-10-24

Graph Theory And Sparse Matrix Computation written by Alan George and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-24 with Mathematics categories.

This IMA Volume in Mathematics and its Appllcations GRAPH THEORY AND SPARSE MATRIX COMPUTATION is based on the proceedings of a workshop that was an integraI part of the 1991- 92 IMA program on "Applied Linear AIgebra." The purpose of the workshop was to bring together people who work in sparse matrix computation with those who conduct research in applied graph theory and grl: l, ph algorithms, in order to foster active cross-fertilization. We are grateful to Richard Brualdi, George Cybenko, Alan Geo ge, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-Iong program. We espeeially thank Alan George, John R. Gilbert, and Joseph W.H. Liu for organizing this workshop and editing the proceedings. The finaneial support of the National Science Foundation made the workshop possible. A vner Friedman Willard Miller. Jr. PREFACE When reality is modeled by computation, linear algebra is often the con nec- tiori between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer. Efficiency demands that every possible advantage be exploited: sparse structure, advanced com- puter architectures, efficient algorithms. Therefore sparse matrix computation knits together threads from linear algebra, parallei computing, data struetures, geometry, and both numerieal and discrete algorithms.

Vectors And Matrices

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Author : Pamela Liebeck
language : en
Publisher: Elsevier
Release Date : 2014-05-09

Vectors And Matrices written by Pamela Liebeck and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.

Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

Matrices And Transformations

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Author : Anthony J. Pettofrezzo
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04

Matrices And Transformations written by Anthony J. Pettofrezzo and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.

This book presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. A Variety of interpretations and applications of the elements and operations considered are included. In particular, the use of matrices in the study of transformations of the plane is stressed. The purpose of this book is to familiarize the reader with the role of matrices in abstract algebraic systems, and to illustrate its effective use as a mathematical tool in geometry. The first two chapters cover the basic concepts of matrix algebra that are important in the study of physics, statistics, economics, engineering, and mathematics. Matrices are considered as elements of an algebra. The concept of a linear transformation of the plane and the use of matrices in discussing such transformations are illustrated in Chapter #. Some aspects of the algebra of transformations and its relation to the algebra of matrices are included here. The last chapter on eigenvalues and eigenvectors contains material usually not found in an introductory treatment of matrix algebra, including an application of the properties of eigenvalues and eigenvectors to the study of the conics. Considerable attention has been paid throughout to the formulation of precise definitions and statements of theorems. The proofs of most of the theorems are included in detail in this book. Matrices and Transformations assumes only that the reader has some understanding of the basic fundamentals of vector algebra. Pettofrezzo gives numerous illustrative examples, practical applications, and intuitive analogies. There are many instructive exercises with answers to the odd-numbered questions at the back. The exercises range from routine computations to proofs of theorems that extend the theory of the subject. Originally written for a series concerned with the mathematical training of teachers, and tested with hundreds of college students, this book can be used as a class or supplementary text for enrichments programs at the high school level, a one-semester college course, individual study, or for in-service programs.