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.
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