Theory Of Generalized Inverses Over Commutative Rings
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Theory Of Generalized Inverses Over Commutative Rings
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Author : K.P.S. Bhaskara Rao
language : en
Publisher: CRC Press
Release Date : 2002-03-21
Theory Of Generalized Inverses Over Commutative Rings written by K.P.S. Bhaskara Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-21 with Mathematics categories.
The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. The subject of generalized inverses of matrices over rings has now reached a state suitable for a comprehensive treatment - this book provides just that, for mathematicians, algebraists and control theorists.
Algebraic Theory Of Generalized Inverses
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Author : Jianlong Chen
language : en
Publisher: Springer Nature
Release Date : 2024-02-28
Algebraic Theory Of Generalized Inverses written by Jianlong Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-28 with Mathematics categories.
Most of the existing monographs on generalized inverses are based on linear algebra tools and geometric methods of Banach (Hilbert) spaces to introduce generalized inverses of complex matrices and operators and their related applications, or focus on generalized inverses of matrices over special rings like division rings and integral domains, and does not include the results in general algebraic structures such as arbitrary rings, semigroups and categories, which are precisely the most general cases. In this book, five important generalized inverses are introduced in these algebraic structures. Moreover, noting that the (pseudo) core inverse was introduced in the last decade and has attracted much attention, this book also covers the very rich research results on it, so as to be a necessary supplement to the existing monographs. This book starts with decompositions of matrices, introduces the basic properties of generalized inverses of matrices, and then discusses generalizedinverses of elements in rings and semigroups, as well as morphisms in categories. The algebraic nature of generalized inverses is presented, and the behavior of generalized inverses are related to the properties of the algebraic system. Scholars and graduate students working on the theory of rings, semigroups and generalized inverses of matrices and operators will find this book helpful.
Generalized Fuzzy Matrices And Relations
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Author : Herbert Toth
language : en
Publisher: World Scientific
Release Date : 2025-02-25
Generalized Fuzzy Matrices And Relations written by Herbert Toth and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-25 with Mathematics categories.
The book provides an overview of the main concepts and results related to fuzzy matrices and fuzzy relations, using 'fuzzy' in a general sense to mean many-valued. This overview, along with numerous references to original contributions dispersed across various journals, serves as a comprehensive guide for further exploration.This volume can be viewed in two ways: (i) as a companion to the author's previous work, 'Relations: Concrete, Abstract, and Applied' (published by WSPC, 2020), but with a distinct emphasis on many-valued concepts; or (ii) as a standalone volume that can be read independently, which necessarily includes some repetition of material from the earlier book as preliminary or reference content.Similar to the previous book, this one does not present new findings but offers a self-contained compilation of known results selected from the extensive research conducted over the past five decades, arranged in a systematic manner.The topics covered in this text have been the subject of intensive research over the last two decades, yet there has been no book publication on this subject for over 15 years. This book aims to bridge that gap.
Model Theory Of Modules Algebras And Categories
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Author : Alberto Facchini
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-05-31
Model Theory Of Modules Algebras And Categories written by Alberto Facchini 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 2019-05-31 with Mathematics categories.
This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28–August 2, 2017, at the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, Italy. Papers contained in this volume cover recent developments in model theory, module theory and category theory, and their intersection.
Linear Algebra Over Commutative Rings
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Author : Bernard R. McDonald
language : en
Publisher: CRC Press
Release Date : 2020-11-26
Linear Algebra Over Commutative Rings written by Bernard R. McDonald and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Handbook Of Linear Algebra Second Edition
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Author : Leslie Hogben
language : en
Publisher: CRC Press
Release Date : 2013-11-26
Handbook Of Linear Algebra Second Edition written by Leslie Hogben and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.
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 updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.
Mathematical Methods For Engineering Applications
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Author : Fatih Yilmaz
language : en
Publisher: Springer Nature
Release Date : 2023-03-08
Mathematical Methods For Engineering Applications written by Fatih Yilmaz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-08 with Mathematics categories.
This proceedings volume convenes selected, peer-reviewed papers presented at the 3rd International Conference on Mathematics and its Applications in Science and Engineering – ICMASE 2022, which was held on July 4–7, 2022 by the Technical University of Civil Engineering of Bucharest, Romania. Works in this volume cover new developments in applications of mathematics in science and engineering, with emphasis on mathematical and computational modeling of real-world problems. Topics range from the use of differential equations to model mechanical structures to the employ of number theory in the development of information security and cryptography. Educational issues specific to the acquisition of mathematical competencies by engineering and science students at all university levels are also touched on. Researchers and university students are the natural audiences for this book, which can be equally appealing to practitioners seeking up-to-date techniques in mathematical applications to different contexts and disciplines.
Relations Concrete Abstract And Applied An Introduction
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Author : Herbert Toth
language : en
Publisher: World Scientific
Release Date : 2020-06-22
Relations Concrete Abstract And Applied An Introduction written by Herbert Toth and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-22 with Mathematics categories.
The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:
Infinite Matrices And Their Recent Applications
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Author : P.N. Shivakumar
language : en
Publisher: Springer
Release Date : 2016-06-20
Infinite Matrices And Their Recent Applications written by P.N. Shivakumar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such as Bessel’s and Mathieu’s equations, viscous fluid flow in doubly connected regions, digital circuit dynamics and eigenvalues of the Laplacian.
Mathematics Across The Iron Curtain
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Author : Christopher Hollings
language : en
Publisher: American Mathematical Society
Release Date : 2014-07-16
Mathematics Across The Iron Curtain written by Christopher Hollings and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-16 with Mathematics categories.
The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.