Infinite Matrices and Their Recent Applications

1. Front Matter

   Pages i-x

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2. Introduction

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

   Pages 1-3

3. Finite Matrices and Their Nonsingularity

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

   Pages 5-25

4. Infinite Linear Equations

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

   Pages 27-39

5. Generalized Inverses: Real or Complex Field

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

   Pages 41-48

6. Generalized Inverses: Quaternions

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

   Pages 49-72

7. M-Matrices over Infinite Dimensional Spaces

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

   Pages 73-85

8. Infinite Linear Programming

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

   Pages 87-92

9. Applications

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

   Pages 93-109

10. Back Matter

    Pages 111-118

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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.

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

“The thin book provides readers with a comprehensive guide to the theory of finite and infinite matrices. … The prospective audience of the monograph includes research students, academicians, researchers. … All topics are thoroughly introduced including historical review and wide references. … the book very carefully prepared and all formulas are well readable.” (Cyril Fischer, zbMATH 1355.15001, 2017)

• Department of Mathematics, University of Manitoba, Winnipeg, Canada

  P.N. Shivakumar, Yang Zhang

• Department of Mathematics, Indian Institute of Technology, Madras, Chennai, India

  K C Sivakumar

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