Combinatorial Matrix Theory And Generalized Inverses Of Matrices

Author : Ravindra B. Bapat,Steve J. Kirkland,K. Manjunatha Prasad,Simo Puntanen
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 48,9 Mb
Release : 2013-02-11
Category : Mathematics
ISBN : 9788132210535

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Combinatorial Matrix Theory and Generalized Inverses of Matrices by Ravindra B. Bapat,Steve J. Kirkland,K. Manjunatha Prasad,Simo Puntanen Pdf

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 : R.E. Cline
Publisher : Springer Science & Business Media
Page : 90 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468467178

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Elements of the Theory of Generalized Inverses of Matrices by R.E. Cline Pdf

The purpose of this monograph is to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. Although results from this active area of research have appeared in a number of excellent graduate level text books since 1971, material for use at the undergraduate level remains fragmented. The basic ideas are so fundamental, however, that they can be used to unify various topics that an undergraduate has seen but perhaps not related. Material in this monograph was first assembled by the author as lecture notes for the senior seminar in mathematics at the University of Tennessee. In this seminar one meeting per week was for a lecture on the subject matter, and another meeting was to permit students to present solutions to exercises. Two major problems were encountered the first quarter the seminar was given. These were that some of the students had had only the required one-quarter course in matrix theory and were not sufficiently familiar with eigenvalues, eigenvectors and related concepts, and that many -v- of the exercises required fortitude. At the suggestion of the UMAP Editor, the approach in the present monograph is (1) to develop the material in terms of full rank factoriza tions and to relegate all discussions using eigenvalues and eigenvectors to exercises, and (2) to include an appendix of hints for exercises.

Author : Bolian Liu,Hong-Jian Lai
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 45,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475731651

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Matrices in Combinatorics and Graph Theory by Bolian Liu,Hong-Jian Lai Pdf

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.

Author : Richard A. Brualdi,Ángeles Carmona,P. van den Driessche,Stephen Kirkland,Dragan Stevanović
Publisher : Birkhäuser
Page : 219 pages
File Size : 51,6 Mb
Release : 2018-03-31
Category : Mathematics
ISBN : 9783319709536

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Combinatorial Matrix Theory by Richard A. Brualdi,Ángeles Carmona,P. van den Driessche,Stephen Kirkland,Dragan Stevanović Pdf

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 : Robert Piziak,P.L. Odell
Publisher : CRC Press
Page : 568 pages
File Size : 47,5 Mb
Release : 2007-02-22
Category : Mathematics
ISBN : 9781420009934

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Matrix Theory by Robert Piziak,P.L. Odell Pdf

In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts whil

Author : Adi Ben-Israel,Thomas Nall Eden Greville
Publisher : Unknown
Page : 418 pages
File Size : 46,5 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015042065931

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Generalized Inverses: Theory and Applications by Adi Ben-Israel,Thomas Nall Eden Greville Pdf

Author : Stephen L. Campbell,Carl D. Meyer
Publisher : SIAM
Page : 289 pages
File Size : 46,6 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780898719048

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Generalized Inverses of Linear Transformations by Stephen L. Campbell,Carl D. Meyer Pdf

Generalized (or pseudo-) inverse concepts routinely appear throughout applied mathematics and engineering, in both research literature and textbooks. Although the basic properties are readily available, some of the more subtle aspects and difficult details of the subject are not well documented or understood. First published in 1979, Generalized Inverses of Linear Transformations remains up-to-date and readable, and it includes chapters on Markov chains and the Drazin inverse methods that have become significant to many problems in applied mathematics. The book provides comprehensive coverage of the mathematical theory of generalized inverses coupled with a wide range of important and practical applications that includes topics in electrical and computer engineering, control and optimization, computing and numerical analysis, statistical estimation, and stochastic processes. Audience: intended for use as a reference by applied scientists and engineers.

Author : Jianlong Chen
Publisher : Springer Nature
Page : 331 pages
File Size : 48,7 Mb
Release : 2024-06-16
Category : Electronic
ISBN : 9789819982851

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Algebraic Theory of Generalized Inverses by Jianlong Chen Pdf

Author : Calyampudi Radhakrishna Rao,Sujit Kumar Mitra
Publisher : John Wiley & Sons
Page : 264 pages
File Size : 48,6 Mb
Release : 1971
Category : Mathematics
ISBN : MINN:31951000012834C

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Generalized Inverse of Matrices and Its Applications by Calyampudi Radhakrishna Rao,Sujit Kumar Mitra Pdf

Notations and preliminaries; Generalized inverse of a matrix; Three basic types of g-inverses; Other special types of g-inverse; Projectors, idempotent matrices and partial isometry; Simulatneous reduction of a pair of herminitian forms; Estimation of parameters in linear models; Conditions for optimality and validity of least-squares theory; Distribution of quadratic forms; Miscellaneous applications of g-inverses; Computational methods; Bibliography on generalized inverses and applications; Index.

Author : Randall E. Cline
Publisher : Unknown
Page : 88 pages
File Size : 46,7 Mb
Release : 1988-01-01
Category : Matrix inversion
ISBN : 0912843136

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Elements of the Theory of Generalized Inverses for Matrices by Randall E. Cline Pdf

Author : Ivan Stanimirović
Publisher : CRC Press
Page : 199 pages
File Size : 50,5 Mb
Release : 2017-12-14
Category : Mathematics
ISBN : 9781351630054

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Computation of Generalized Matrix Inverses and Applications by Ivan Stanimirović Pdf

This volume offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra. The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i,j,...,k} inverse and the Moore–Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore–Penrose’s inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization. The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed. It covers several methods, such as methods based on full-rank factorization, Leverrier–Faddeev method, method of Zhukovski, and variations of the partitioning method.

Author : K Manjunatha Prasad,Ravindra B. Bapat,Steve Kirkland
Publisher : Manipal Universal Press
Page : 246 pages
File Size : 45,9 Mb
Release : 2012
Category : Combinatorial number theory
ISBN : 8192275965

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Lectures on Matrix and Graph Methods by K Manjunatha Prasad,Ravindra B. Bapat,Steve Kirkland Pdf

Papers presented at the International Workshop and Conference on Combinatorial Matrix Theory & Generalized Inverses of Matrices, organized by Department of Statistics, Manipal University during 2-7 January 2012.

Author : Changjiang BU,Lizhu SUN,Yimin WEI
Publisher : EDP Sciences
Page : 234 pages
File Size : 54,8 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9782759826001

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Sign Pattern for Generalized Inverses by Changjiang BU,Lizhu SUN,Yimin WEI Pdf

This book addresses recent developments in sign patterns for generalized inverses. The fundamental importance of the fields is obvious, since they are related with qualitative analysis of linear systems and combinatorial matrix theory. The book provides both introductory materials and discussions to the areas in sign patterns for Moore–Penrose inverse, Drazin inverse and tensors. It is intended to convey results to the senior students and readers in pure and applied linear algebra, and combinatorial matrix theory. Changjiang BU is a Professor at the College of Mathematical Sciences, Harbin Engineering University, who works on the graph theory and generalized inverses. He is the author of more than 100 papers in the international journals and one monograph. Lizhu SUN is an Associate Professor at the College of Mathematical Sciences, Harbin Engineering University, who works on the graph theory and multilinear algebra. She is the author of 25 research papers. Yimin WEI is a Professor at the School of Mathematical Sciences, Fudan University, who works on the numerical linear algebra and multilinear algebra. He is the author of more than 150 papers in the international journals and six monographs published by Science Press, Elsevier, Springer and World Scientific., etc.

Author : Richard A. Brualdi,Dragos Cvetkovic
Publisher : CRC Press
Page : 288 pages
File Size : 55,5 Mb
Release : 2008-08-06
Category : Mathematics
ISBN : 1420082248

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A Combinatorial Approach to Matrix Theory and Its Applications by Richard A. Brualdi,Dragos Cvetkovic Pdf

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.

Author : Thomas Loris Boullion,Patrick L. Odell
Publisher : Unknown
Page : 362 pages
File Size : 49,6 Mb
Release : 1968
Category : Matrices
ISBN : UVA:X001450064

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Theory and Application of Generalized Inverses of Matrices by Thomas Loris Boullion,Patrick L. Odell Pdf