This text is a self-contained introduction to some problems for Toeplitz matrices that are placed in the borderland between linear algebra and functional analysis. The text looks at Toeplitz matrices with rational symbols, and focuses attention on the asymptotic behavior of the singular values, which includes the behavior of the norms, the norms of the inverses, and the condition numbers as special cases. The text illustrates that the asymptotics of several linear algebra characteristics depend in a fascinating way on functional analytic properties of infinite matrices. Many convergence results can very comfortably be obtained by working with appropriate C*-algebras, while refinements of these results, for example, estimates of the convergence speed, nevertheless require hard analysis.
- ISBN10 3764362901
- ISBN13 9783764362904
- Publish Date 1 June 2000
- Publish Status Out of Stock
- Out of Print 2 June 2021
- Publish Country CH
- Imprint Birkhauser Verlag AG
- Format Paperback (US Trade)
- Pages 128
- Language English