Linear Algebra and its Applications 343–344 (2002) 1–4 www.elsevier.com/locate/laa Preface Special Issue on Structured and Infinite Systems of Linear Equations Patrick Dewilde a , Vadim Olshevsky b , Ali H. Sayed c a DIMES, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands b Department of Mathematics and Computer Science, Georgia State University, University Plaza, Atlanta, GA 30303, USA c Rm 44-123A Engr. IV Bldg, Department of Electrical Engineering, University of California, Los Angeles, CA 90095-1594, USA Interest in ‘structured and infinite systems of linear equations’ has been there for a long time, ever since the 18th century. While nowadays we tend to study finite-di- mensional structured linear equations almost in separation of what we would regard as more sophisticated (or even more demanding) infinite-dimensional structured sys- tems, it is worth stressing that, in retrospect, both issues of structure and infinite dimensionality have manifested themselves jointly in the earliest works on such top- ics. This is clear from the contributions of a handful of distinguished mathematicians from the 18th, 19th and early 20th centuries, including Kronecker, Carathéodory, Toeplitz, Schur, Nevanlinna, Riesz, Szegö and others, in the areas of moment prob- lems, interpolation theory, orthogonal polynomials and spaces of analytic functions. In most of these earlier investigations, the notions of structure and infinite dimensi- onality are handled jointly through the concepts of symbols or generating functions. Kronecker, for example, gave a characterization of Toeplitz matrices whose symbol is rational—namely that a related Hankel matrix should have finite rank. For such matrices, efficient computing schemes can be set up that exploit the ‘system struc- ture’ of the matrix. Although not used much in the practice of handling finite Toeplitz matrices, the ‘realization method’ implicitly initiated by Kronecker turns out to be extremely valuable to study infinite Toeplitz matrices, and certainly leads to finite and efficient calculations for systems of equations induced by such matrices. Very deep insights in the properties of infinite Toeplitz systems were developed at the end of the 19th century and in the beginning of the 20th century, in what is now known as E-mail addresses: dewilde@dimes.tudelft.nl (P. Dewilde), volshevsky@cs.gsu.edu (V. Olshevsky), sayed@biruni.icsl.ucla.edu (A.H. Sayed). 0024-3795/01/$ - see front matter  2001 Elsevier Science Inc. All rights reserved. PII:S0024-3795(01)00545-6