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.
