Infinite matrices and their recent applications / by P.N. Shivakumar, K.C. Sivakumar, Yang Zhang.

Format:

Book

Author/Creator:

Shivakumar, P.N., Author.

Sivakumar, K.C., Author.

Zhang, Yang, Author.

Language:

English

Subjects (All):

Matrix theory.

Algebra.

Linear and Multilinear Algebras, Matrix Theory.

Local Subjects:

Linear and Multilinear Algebras, Matrix Theory.

Physical Description:

1 online resource (X, 118 p.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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.

Contents:

Introduction

Finite Matrices and their Nonsingularity

Infinite Linear Equations

Generalized Inverses: Real or Complex Field

Generalized Inverses: Quaternions

M-matrices over Infinite Dimensional Spaces

Infinite Linear Programming

Applications. .

Notes:

Includes bibliographical references and index.

ISBN:

3-319-30180-2