Finite and Infinite Matrices and Some Applications
Author | : Kim Ho Chew |
Publisher | : |
Total Pages | : |
Release | : 2012 |
Genre | : |
ISBN | : |
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Author | : Kim Ho Chew |
Publisher | : |
Total Pages | : |
Release | : 2012 |
Genre | : |
ISBN | : |
Author | : Chew, Kim Ho |
Publisher | : c1975 |
Total Pages | : 112 |
Release | : 1975 |
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ISBN | : |
Author | : Chuanxiang Ji |
Publisher | : |
Total Pages | : 0 |
Release | : 1998 |
Genre | : |
ISBN | : |
Author | : P.N. Shivakumar |
Publisher | : Springer |
Total Pages | : 124 |
Release | : 2016-06-20 |
Genre | : Mathematics |
ISBN | : 3319301802 |
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 |
Total Pages | : 203 |
Release | : 2006-11-10 |
Genre | : Mathematics |
ISBN | : 3764377674 |
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 | : |
Publisher | : |
Total Pages | : |
Release | : 1998 |
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ISBN | : |
Author | : Richard G. Cooke |
Publisher | : Courier Corporation |
Total Pages | : 370 |
Release | : 2014-06-10 |
Genre | : Mathematics |
ISBN | : 0486795063 |
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 | : Neelacanta Sthanumoorthy |
Publisher | : Academic Press |
Total Pages | : 514 |
Release | : 2016-04-26 |
Genre | : Mathematics |
ISBN | : 012804683X |
Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras
Author | : Bertram Wehrfritz |
Publisher | : Springer Science & Business Media |
Total Pages | : 243 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642870813 |
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 | : Charles Swartz |
Publisher | : World Scientific |
Total Pages | : 222 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9810227361 |
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.