Infinite Matrices And Their Recent Applications

Author : P.N. Shivakumar,K.C. Sivakumar,Yang Zhang
Publisher : Springer
Page : 118 pages
File Size : 53,5 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9783319301808

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Infinite Matrices and Their Recent Applications by P.N. Shivakumar,K.C. Sivakumar,Yang Zhang Pdf

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.

Author : Marko Lindner
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 47,7 Mb
Release : 2006-11-10
Category : Mathematics
ISBN : 9783764377670

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Infinite Matrices and their Finite Sections by Marko Lindner Pdf

This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. The main concepts presented are invertibility at infinity (closely related to Fredholmness), limit operators, and the stability and convergence of finite matrix approximations. Concrete examples are used to illustrate the results throughout, including discrete Schrödinger operators and integral and boundary integral operators arising in mathematical physics and engineering.

Author : Richard G. Cooke
Publisher : Courier Corporation
Page : 370 pages
File Size : 40,8 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486795065

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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.

Author : Ivor John Maddox
Publisher : Unknown
Page : 128 pages
File Size : 54,7 Mb
Release : 1980
Category : Electronic
ISBN : LCCN:80011702

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Infinite Matrices of Operators by Ivor John Maddox Pdf

Author : I. J. Maddox
Publisher : Unknown
Page : 132 pages
File Size : 51,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662174081

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Infinite Matrices of Operators by I. J. Maddox Pdf

Author : Madhumangal Pal
Publisher : Springer Nature
Page : 494 pages
File Size : 40,5 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031569364

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Recent Developments of Fuzzy Matrix Theory and Applications by Madhumangal Pal Pdf

Author : Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 51,8 Mb
Release : 2011
Category : Infinite matrices
ISBN : 9780821852484

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Iterated Function Systems, Moments, and Transformations of Infinite Matrices by Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman Pdf

The authors study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Their main object of study is the infinite matrix which encodes all the moment data of a Borel measure on $\mathbb{R}^d$ or $\mathbb{C}$. To encode the salient features of a given IFS into precise moment data, they establish an interdependence between IFS equilibrium measures, the encoding of the sequence of moments of these measures into operators, and a new correspondence between the IFS moments and this family of operators in Hilbert space. For a given IFS, the authors' aim is to establish a functorial correspondence in such a way that the geometric transformations of the IFS turn into transformations of moment matrices, or rather transformations of the operators that are associated with them.

Author : Charles Swartz
Publisher : World Scientific
Page : 222 pages
File Size : 42,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9789810227364

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Infinite Matrices and the Gliding Hump by Charles Swartz Pdf

These notes present a theorem on infinite matrices with values in a topological group due to P Antosik and J Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.

Author : Bertram Wehrfritz
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642870811

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Infinite Linear Groups by Bertram Wehrfritz Pdf

By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.

Author : Franz E. Hohn
Publisher : Courier Corporation
Page : 562 pages
File Size : 55,8 Mb
Release : 2013-02-19
Category : Mathematics
ISBN : 9780486143729

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Elementary Matrix Algebra by Franz E. Hohn Pdf

This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations — homogeneous or nonhomogeneous — and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology. Other subjects include the complete treatment of the structure of the solution space of a system of linear equations, the most commonly used properties of determinants, and linear operators and linear transformations of coordinates. Considerably more material than can be offered in a one-semester course appears here; this comprehensive volume by Franz E. Hohn, Professor of Mathematics at the University of Illinois for many years, provides instructors with a wide range of choices in order to meet differing interests and to accommodate students with varying backgrounds.

Author : R. G. Cooke
Publisher : Unknown
Page : 128 pages
File Size : 41,7 Mb
Release : 1972
Category : Electronic
ISBN : OCLC:500321507

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Infinite Matrices and Sequence Spaces by R. G. Cooke Pdf

Author : J. S. Lomont
Publisher : Academic Press
Page : 359 pages
File Size : 53,5 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483268965

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Applications of Finite Groups by J. S. Lomont Pdf

Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.

Author : Anonim
Publisher : Unknown
Page : 360 pages
File Size : 48,7 Mb
Release : 1950
Category : Electronic
ISBN : OCLC:1176145042

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Infinite Matrices and Sequence Spaces by Anonim Pdf

Author : Dinh Van Huynh,International conference on algebra and its applications,Surender Kumar Jain
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 48,7 Mb
Release : 2000
Category : Algebra
ISBN : 9780821819500

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Algebra and Its Applications by Dinh Van Huynh,International conference on algebra and its applications,Surender Kumar Jain Pdf

Among all areas of mathematics, algebra is one of the best suited to find applications within the frame of our booming technological society. The thirty-eight articles in this volume encompass the proceedings of the International Conference on Algebra and Its Applications (Athens, OH, 1999), which explored the applications and interplay among the disciplines of ring theory, linear algebra, and coding theory. The presentations collected here reflect the dialogue between mathematicians involved in theoretical aspects of algebra and mathematicians involved in solving problems where state-of-the-art research tools may be used and applied. This Contemporary Mathematics series volume communicates the potential for collaboration among those interested in exploring the wealth of applications for abstract algebra in fields such as information and coding. The expository papers would serve well as supplemental reading in graduate seminars.

Author : Richard G. Cooke
Publisher : Unknown
Page : 347 pages
File Size : 54,9 Mb
Release : 1955
Category : Electronic
ISBN : OCLC:310729692

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Infinite Matrices and Sequence Spaces by Richard G. Cooke Pdf