In this chapter, the matrix transformations in sequence spaces are studied and
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 are given.
Matrix transformations between sequence spaces, ordinary, absolute
and strong summability, KOjima-Schur theorem, Silverman-Toeplitz theorem,
Schur's theorem, algebra, normed and Banach algebra, characteristic of a matrix,
sequence-to-sequence, series-to-sequence, series-to-series and sequence-to-series matrix
transformations, dual summability methods, arithmetics, Cesàro, Euler, Riesz
and Nörlund means, Taylor, Ar, Hausdor, Borel and Abel matrices.