Group Inverses Of M Matrices And Their Applications

Author : Stephen J. Kirkland,Michael Neumann
Publisher : CRC Press
Page : 334 pages
File Size : 53,6 Mb
Release : 2012-12-18
Category : Mathematics
ISBN : 9781439888582

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Group Inverses of M-Matrices and Their Applications by Stephen J. Kirkland,Michael Neumann Pdf

Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix functions and apply the formulas to matrices arising in a demographic setting, including the class of Leslie matrices. With a focus on Markov chains, the text shows how the group inverse of an appropriate M-matrix is used in the perturbation analysis of the stationary distribution vector as well as in the derivation of a bound for the asymptotic convergence rate of the underlying Markov chain. It also illustrates how to use the group inverse to compute and analyze the mean first passage matrix for a Markov chain. The final chapters focus on the Laplacian matrix for an undirected graph and compare approaches for computing the group inverse. Collecting diverse results into a single volume, this self-contained book emphasizes the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. It shows how group inverses offer valuable insight into each of these areas.

Author : K. J. Horadam
Publisher : Princeton University Press
Page : 280 pages
File Size : 54,9 Mb
Release : 2012-01-06
Category : Mathematics
ISBN : 9781400842902

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Hadamard Matrices and Their Applications by K. J. Horadam Pdf

In Hadamard Matrices and Their Applications, K. J. Horadam provides the first unified account of cocyclic Hadamard matrices and their applications in signal and data processing. This original work is based on the development of an algebraic link between Hadamard matrices and the cohomology of finite groups that was discovered fifteen years ago. The book translates physical applications into terms a pure mathematician will appreciate, and theoretical structures into ones an applied mathematician, computer scientist, or communications engineer can adapt and use. The first half of the book explains the state of our knowledge of Hadamard matrices and two important generalizations: matrices with group entries and multidimensional Hadamard arrays. It focuses on their applications in engineering and computer science, as signal transforms, spreading sequences, error-correcting codes, and cryptographic primitives. The book's second half presents the new results in cocyclic Hadamard matrices and their applications. Full expression of this theory has been realized only recently, in the Five-fold Constellation. This identifies cocyclic generalized Hadamard matrices with particular "stars" in four other areas of mathematics and engineering: group cohomology, incidence structures, combinatorics, and signal correlation. Pointing the way to possible new developments in a field ripe for further research, this book formulates and discusses ninety open questions.

Author : Leslie Hogben
Publisher : CRC Press
Page : 1906 pages
File Size : 44,7 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9781498785600

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Handbook of Linear Algebra by Leslie Hogben Pdf

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and

Author : Yimin Wei,Predrag Stanimirovic,Marko Petkovic
Publisher : World Scientific
Page : 472 pages
File Size : 40,5 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9789813238688

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Numerical And Symbolic Computations Of Generalized Inverses by Yimin Wei,Predrag Stanimirovic,Marko Petkovic Pdf

We introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed in other book, which is important for numerical-symbolic computations.

Author : Claude Dellacherie,Servet Martinez,Jaime San Martin
Publisher : Springer
Page : 236 pages
File Size : 48,7 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 3319102990

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Inverse M-Matrices and Ultrametric Matrices by Claude Dellacherie,Servet Martinez,Jaime San Martin Pdf

The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.

Author : Gaogao Dong,Saray Shai,Yongxiang Xia,Dongli Duan
Publisher : Frontiers Media SA
Page : 213 pages
File Size : 50,6 Mb
Release : 2022-08-17
Category : Science
ISBN : 9782889767823

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Network Resilience and Robustness: Theory and Applications by Gaogao Dong,Saray Shai,Yongxiang Xia,Dongli Duan Pdf

Author : Stephen L. Campbell,Carl D. Meyer
Publisher : SIAM
Page : 289 pages
File Size : 50,5 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 : Adi Ben-Israel,Thomas N.E. Greville
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 43,8 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216348

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Generalized Inverses by Adi Ben-Israel,Thomas N.E. Greville Pdf

This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.

Author : Guorong Wang,Yimin Wei,Sanzheng Qiao
Publisher : Springer
Page : 378 pages
File Size : 42,7 Mb
Release : 2018-05-12
Category : Mathematics
ISBN : 9789811301469

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Generalized Inverses: Theory and Computations by Guorong Wang,Yimin Wei,Sanzheng Qiao Pdf

This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

Author : Sujit Kumar Mitra,P. Bhimasankaram,Saroj B. Malik
Publisher : World Scientific
Page : 463 pages
File Size : 52,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812838445

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Matrix Partial Orders, Shorted Operators and Applications by Sujit Kumar Mitra,P. Bhimasankaram,Saroj B. Malik Pdf

The present monograph on matrix partial orders, appearing for the first time, is a unique presentation of many partial orders on matrices that have fascinated mathematicians for their beauty and applied scientists for their wide-ranging application potential. Except for the Lwner order, the partial orders considered are relatively new and came into being in the late 1970s. After a detailed introduction to generalized inverses and decompositions, the three basic partial orders namely, the minus, the sharp and the star and the corresponding one-sided orders are presented using various generalized inverses. The authors then give a unified theory of all these partial orders. This is followed by a study of the Lwner order and a limited treatment of majorization (there is an abundance of literature available on majorization). The authors also study the parallel sums and shorted matrices, the latter being studied at great length. Partial orders of modified matrices are a new addition. Finally, applications are given in statistics and electrical network theory.

Author : Anonim
Publisher : Unknown
Page : 960 pages
File Size : 42,8 Mb
Release : 2007
Category : Mathematics
ISBN : UCSD:31822036024826

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SIAM Journal on Matrix Analysis and Applications by Anonim Pdf

Author : Dragana S. Cvetković‐Ilić,Yimin Wei
Publisher : Springer
Page : 194 pages
File Size : 43,9 Mb
Release : 2017-10-07
Category : Mathematics
ISBN : 9789811063497

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Algebraic Properties of Generalized Inverses by Dragana S. Cvetković‐Ilić,Yimin Wei Pdf

This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.

Author : Abraham Berman,Robert J. Plemmons
Publisher : Academic Press
Page : 337 pages
File Size : 49,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260860

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Nonnegative Matrices in the Mathematical Sciences by Abraham Berman,Robert J. Plemmons Pdf

Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.

Author : Jeffrey Hunter
Publisher : Unknown
Page : 52 pages
File Size : 46,9 Mb
Release : 1988
Category : Electronic
ISBN : CORNELL:31924074846928

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Parametric Forms for Generalized Inverses of Markovian Kernels and Their Applications by Jeffrey Hunter Pdf

Author : Alston Scott Householder
Publisher : Unknown
Page : 552 pages
File Size : 40,6 Mb
Release : 1972
Category : Algebra
ISBN : STANFORD:36105033326336

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KWIC Index for Numerical Algebra by Alston Scott Householder Pdf