Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis

This text is a self-contained 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, which includes the behaviour of the norms, the norms of the inverses, and the condition numbers as special cases.

The text aims to illustrate that the asymptotics of several linear algebra characteristics.