Toeplitz Matrices, Asymptotic Linear Algebra, And Functional Analysis; Author: Bottcher, Albrecht; Joint Author: Grudsky, Sergei M.; Paperback

Author: Bottcher, Albrecht; Joint Author: Grudsky, Sergei M.
Paperback; Bibliography
104 pages
Published: April 2000
Birkhauser Verlag AG
ISBN: 3764362901

This is a self-contained introduction to problems for Toeplitz matrices. The authors present the topic in relation to the border between linear algebra and functional analysis and illustrate that the asymptotics of several linear algebra characteristics depend, in a fascinating way, on functional analytic properties of infinite matrices. The book is addressed to beginners in the field requiring only familiarity with the basics of real and complex analysis, linear algebra, and functional analysis. Almost all results presented are accompanied by full proofs.This text offers an introduction to some problems of Toeplitz matrices that are placed in the borderland between linear algebra and functional analysis. The author's confine themselves to Toeplitz matrices with rational symbols, and focus on the asymptotic behaviour of the singular values.