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Infinite Matrices and Their Recent Applications

  • P.N. Shivakumar
  • K C Sivakumar
  • Yang Zhang

Table of contents

  1. Front Matter
    Pages i-x
  2. P. N. Shivakumar, K. C. Sivakumar, Yang Zhang
    Pages 1-3
  3. P. N. Shivakumar, K. C. Sivakumar, Yang Zhang
    Pages 5-25
  4. P. N. Shivakumar, K. C. Sivakumar, Yang Zhang
    Pages 27-39
  5. P. N. Shivakumar, K. C. Sivakumar, Yang Zhang
    Pages 41-48
  6. P. N. Shivakumar, K. C. Sivakumar, Yang Zhang
    Pages 49-72
  7. P. N. Shivakumar, K. C. Sivakumar, Yang Zhang
    Pages 73-85
  8. P. N. Shivakumar, K. C. Sivakumar, Yang Zhang
    Pages 87-92
  9. P. N. Shivakumar, K. C. Sivakumar, Yang Zhang
    Pages 93-109
  10. Back Matter
    Pages 111-118

About this book

Introduction

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.

Keywords

Finite Matrices Quaternions Infinite Linear Systems M-Matrices Dimensional Spaces Infinite Matrices Theory of finite and infinite matrices Truncations and linear operator theory

Authors and affiliations

  • P.N. Shivakumar
    • 1
  • K C Sivakumar
    • 2
  • Yang Zhang
    • 3
  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada
  2. 2.Department of MathematicsIndian Institute of Technology, MadrasChennaiIndia
  3. 3.Department of MathematicsUniversity of ManitobaWinnipegCanada

Bibliographic information