Formal Matrices

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Formal Matrices

Piotr Krylov,Askar Tuganbaev
Formal Matrices Book PDF

Author : Piotr Krylov,Askar Tuganbaev
Publisher : Springer
Page : 156 pages
File Size : 49,7 Mb
Release : 2017-03-30
Category : Mathematics
ISBN : 9783319539072

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Formal Matrices by Piotr Krylov,Askar Tuganbaev Pdf

This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.

Introduction to Matrices and Vectors

Jacob T. Schwartz
Introduction to Matrices and Vectors Book PDF

Author : Jacob T. Schwartz
Publisher : Courier Corporation
Page : 198 pages
File Size : 53,7 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0486420000

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Introduction to Matrices and Vectors by Jacob T. Schwartz Pdf

Concise undergraduate text focuses on problem solving, rather than elaborate proofs. The first three chapters present the basics of matrices, including addition, multiplication, and division. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. 1961 edition. 20 black-and-white illustrations.

Random Matrices, Random Processes and Integrable Systems

John Harnad
Random Matrices Random Processes and Integrable Systems Book PDF

Author : John Harnad
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 55,7 Mb
Release : 2011-05-06
Category : Science
ISBN : 9781441995148

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Random Matrices, Random Processes and Integrable Systems by John Harnad Pdf

This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.

Combinatorial Matrix Theory

Richard A. Brualdi,Herbert J. Ryser
Combinatorial Matrix Theory Book PDF

Author : Richard A. Brualdi,Herbert J. Ryser
Publisher : Cambridge University Press
Page : 384 pages
File Size : 45,5 Mb
Release : 1991-07-26
Category : Mathematics
ISBN : 0521322650

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Combinatorial Matrix Theory by Richard A. Brualdi,Herbert J. Ryser Pdf

This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves.

Advanced Multivariate Statistics with Matrices

Tõnu Kollo,D. von Rosen
Advanced Multivariate Statistics with Matrices Book PDF

Author : Tõnu Kollo,D. von Rosen
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 51,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9781402034190

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Advanced Multivariate Statistics with Matrices by Tõnu Kollo,D. von Rosen Pdf

The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course ”Matrices in Statistics” at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course ”Multivariate Asymptotic Statistics” in spring 2002. An advanced course ”Multivariate Linear Models” may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.

Deformations of Nilpotent Matrices over Rings and Reduction of Analytic Families of Meromorphic Differential Equations

Donald G. Babbitt,V. S. Varadarajan
Deformations of Nilpotent Matrices over Rings and Reduction of Analytic Families of Meromorphic Differential Equations Book PDF

Author : Donald G. Babbitt,V. S. Varadarajan
Publisher : American Mathematical Soc.
Page : 147 pages
File Size : 49,7 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821823262

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Deformations of Nilpotent Matrices over Rings and Reduction of Analytic Families of Meromorphic Differential Equations by Donald G. Babbitt,V. S. Varadarajan Pdf

This paper studies the reduction theory of analytic parametric families of systems of linear meromorphic differential equations in the neighborhood of an irregular singularity.

Algebraic and Geometric Aspects of Integrable Systems and Random Matrices

Anton Dzhamay,Ken'ichi Maruno,Virgil U. Pierce
Algebraic and Geometric Aspects of Integrable Systems and Random Matrices Book PDF

Author : Anton Dzhamay,Ken'ichi Maruno,Virgil U. Pierce
Publisher : American Mathematical Soc.
Page : 363 pages
File Size : 48,5 Mb
Release : 2013-06-26
Category : Mathematics
ISBN : 9780821887479

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Algebraic and Geometric Aspects of Integrable Systems and Random Matrices by Anton Dzhamay,Ken'ichi Maruno,Virgil U. Pierce Pdf

This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates

Matrices and Matroids for Systems Analysis

Kazuo Murota
Matrices and Matroids for Systems Analysis Book PDF

Author : Kazuo Murota
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 45,9 Mb
Release : 2009-10-27
Category : Mathematics
ISBN : 9783642039942

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Matrices and Matroids for Systems Analysis by Kazuo Murota Pdf

A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "...The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006

From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems

Daizhan Cheng
From Dimension Free Matrix Theory to Cross Dimensional Dynamic Systems Book PDF

Author : Daizhan Cheng
Publisher : Academic Press
Page : 364 pages
File Size : 45,6 Mb
Release : 2019-05-18
Category : Mathematics
ISBN : 9780128178027

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From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems by Daizhan Cheng Pdf

From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems feature prominently across many disciplines, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and biosystems, deep learning, IT, and information-based engineering applications. Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems. Offers potential applications to the analysis and control of new dimension-varying systems. Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.

Thinking Arabic Translation

James Dickins,Sándor Hervey,Ian Higgins
Thinking Arabic Translation Book PDF

Author : James Dickins,Sándor Hervey,Ian Higgins
Publisher : Routledge
Page : 333 pages
File Size : 50,5 Mb
Release : 2016-10-04
Category : Foreign Language Study
ISBN : 9781315471556

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Thinking Arabic Translation by James Dickins,Sándor Hervey,Ian Higgins Pdf

Thinking Arabic Translation is an indispensable book for linguists who want to develop their Arabic-to-English translation skills. Clear explanations, discussions, examples and exercises enable students to acquire the skills necessary for tackling a broad range of translation problems. The book has a practical orientation, addressing key issues for translators, such as cultural differences, genre, and revision and editing. It is a book on translation method, drawing on a range of notions from linguistics and translation theory to encourage thoughtful consideration of possible solutions to practical problems. This new edition includes: • new material in almost all chapters • a new chapter on parallelism • two new chapters on technical translation: botanical and Islamic finance texts • new and up-to-date examples from all types of translation, covering broad issues that have emerged in the Arab world in recent years • texts drawn from a wide variety of writing types, including newspapers, prose fiction, poetry, tourist material, scientific texts, financial texts, recipes, academic writing, constitutions and political speeches • at least three full-length practical translation exercises in each chapter to complement the discussions and consolidate learning. In addition to the updated Tutor’s Handbook, a Supplement, containing textual material and practical exercises aimed at further developing the translation issues discussed in the main text, and a Tutor’s Handbook to the Supplement, are available at www.routledge.com/cw/dickins. Thinking Arabic Translation is key reading for advanced students wishing to perfect their language skills or considering a career in translation.

Formalization of Complex Analysis and Matrix Theory

Zhiping Shi,Yong Guan,Ximeng Li
Formalization of Complex Analysis and Matrix Theory Book PDF

Author : Zhiping Shi,Yong Guan,Ximeng Li
Publisher : Springer Nature
Page : 172 pages
File Size : 53,6 Mb
Release : 2020-08-10
Category : Mathematics
ISBN : 9789811572616

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Formalization of Complex Analysis and Matrix Theory by Zhiping Shi,Yong Guan,Ximeng Li Pdf

This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.

Conceptual Structures: Inspiration and Application

Henrik Schärfe,Pascal Hitzler,Peter Ohrstrom
Conceptual Structures Inspiration and Application Book PDF

Author : Henrik Schärfe,Pascal Hitzler,Peter Ohrstrom
Publisher : Springer
Page : 465 pages
File Size : 47,5 Mb
Release : 2006-08-29
Category : Computers
ISBN : 9783540359029

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Conceptual Structures: Inspiration and Application by Henrik Schärfe,Pascal Hitzler,Peter Ohrstrom Pdf

This book constitutes the refereed proceedings of the 14th International Conference on Conceptual Structures, ICCS 2006, held in Aalborg, Denmark in July 2006. The volume presents 24 revised full papers, together with 6 invited papers. The papers address topics such as conceptual structures; their interplay with language, semantics and pragmatics; formal methods for concept analysis and contextual logic, modeling, representation, and visualization of concepts; conceptual knowledge acquisition and more.

Infinite Matrices and Sequence Spaces

Richard G. Cooke
Infinite Matrices and Sequence Spaces Book PDF

Author : Richard G. Cooke
Publisher : Courier Corporation
Page : 370 pages
File Size : 40,9 Mb
Release : 2014-07-16
Category : Mathematics
ISBN : 9780486780832

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Infinite Matrices and Sequence Spaces by Richard G. Cooke Pdf

Clear, correct summation of basic results on general behavior of infinite matrices features three introductory chapters leading to applications related to summability of divergent sequences and series. Nearly 200 examples. 1950 edition.

Matrices and Graphs Stability Problems in Mathematical Ecology

D. Logofet
Matrices and Graphs Stability Problems in Mathematical Ecology Book PDF

Author : D. Logofet
Publisher : CRC Press
Page : 320 pages
File Size : 46,9 Mb
Release : 2018-02-01
Category : Science
ISBN : 9781351082778

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Matrices and Graphs Stability Problems in Mathematical Ecology by D. Logofet Pdf

Intuitive ideas of stability in dynamics of a biological population, community, or ecosystem can be formalized in the framework of corresponding mathematical models. These are often represented by systems of ordinary differential equations or difference equations. Matrices and Graphs covers achievements in the field using concepts from matrix theory and graph theory. The book effectively surveys applications of mathematical results pertinent to issues of theoretical and applied ecology. The only mathematical prerequisite for using Matrices and Graphs is a working knowledge of linear algebra and matrices. The book is ideal for biomathematicians, ecologists, and applied mathematicians doing research on dynamic behavior of model populations and communities consisting of multi-component systems. It will also be valuable as a text for a graduate-level topics course in applied math or mathematical ecology.

Structured Matrices in Mathematics, Computer Science, and Engineering I

Vadim Olshevsky
Structured Matrices in Mathematics Computer Science and Engineering I Book PDF

Author : Vadim Olshevsky
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 45,7 Mb
Release : 2001
Category : Matrices
ISBN : 9780821819210

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Structured Matrices in Mathematics, Computer Science, and Engineering I by Vadim Olshevsky Pdf

"The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.