Formal Matrices
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Formal Matrices
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Author : Piotr Krylov
language : en
Publisher: Springer
Release Date : 2017-03-30
Formal Matrices written by Piotr Krylov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-30 with Mathematics categories.
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
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Author : Jacob T. Schwartz
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
Introduction To Matrices And Vectors written by Jacob T. Schwartz and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
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
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Author : John Harnad
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-06
Random Matrices Random Processes And Integrable Systems written by John Harnad 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 2011-05-06 with Science categories.
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
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Author : Richard A. Brualdi
language : en
Publisher: Cambridge University Press
Release Date : 1991-07-26
Combinatorial Matrix Theory written by Richard A. Brualdi 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 1991-07-26 with Mathematics categories.
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.
Deformations Of Nilpotent Matrices Over Rings And Reduction Of Analytic Families Of Meromorphic Differential Equations
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Author : Donald G. Babbitt
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Deformations Of Nilpotent Matrices Over Rings And Reduction Of Analytic Families Of Meromorphic Differential Equations written by Donald G. Babbitt 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 1985 with Mathematics categories.
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
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Author : Anton Dzhamay
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-26
Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices written by Anton Dzhamay 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 2013-06-26 with Mathematics categories.
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
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Author : Kazuo Murota
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-27
Matrices And Matroids For Systems Analysis written by Kazuo Murota 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 2009-10-27 with Mathematics categories.
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
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Author : Daizhan Cheng
language : en
Publisher: Academic Press
Release Date : 2019-05-18
From Dimension Free Matrix Theory To Cross Dimensional Dynamic Systems written by Daizhan Cheng and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-18 with Mathematics categories.
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.
Formalization Of Complex Analysis And Matrix Theory
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Author : Zhiping Shi
language : en
Publisher: Springer Nature
Release Date : 2020-08-10
Formalization Of Complex Analysis And Matrix Theory written by Zhiping Shi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-10 with Mathematics categories.
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
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Author : Henrik Schärfe
language : en
Publisher: Springer
Release Date : 2006-08-29
Conceptual Structures Inspiration And Application written by Henrik Schärfe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-29 with Computers categories.
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.