ABSTRACT
This chapter explains the matrix transformations in sequence spaces and gives the characterizations of the classes of Schur, Kojima and Toeplitz matrices together with their versions for the series-to-sequence, sequence-to-series and series-to-series matrix transformations. In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So, the theory of matrix transformations has always been of great interest in the study of sequence spaces. The study of the general theory of matrix transformations was motivated by special results in the summability theory. Summability is a wide field of mathematics, mainly in analysis and functional analysis, and has many applications, for instance in numerical analysis to speed up the rate of convergence in operator theory, the theory of orthogonal series and approximation theory. The classical summability theory deals with the generalization of the convergence of sequences or series of real or complex numbers.
