The classical Cesaro sequence space and its algebraic dual and related

matrix transformations were introduced and studied by various authors like Shiue [25], Leibowitz [26], Lim [24], Khan and Khan [27],[28], Khan and Rahman [22], Johnson and Mohapatra [29], Rahman and Karim [30], etc.

Furthermore, they determined the [alpha]-, [beta]([??])-, and [gamma]-duals of some new double sequence spaces and characterized some classes of four-dimensional

matrix transformations related to the new double sequence spaces.

The warning about over-actuated systems is given because the input/output rectangular

matrix transformations needed in this case may assume a rigid platform.

In [9-11], the authors discuss the

matrix transformations that preserve (p, q)-convexity of sequences in the case of a lower triangular matrix with a particular type of

matrix transformation.

The above

matrix transformations in Step 1 can be expressed by the function [F.sub.1] ([A.sub.ij]).

Many authors have extensively developed the theory of the

matrix transformations between some sequence spaces; we refer the reader to [1-6].

Mathai, Jacobians of

Matrix Transformations and Functions of Matrix Arguments, World Scientific, 1997.

Some

matrix transformations of convex and paranormed sequence spaces into the spaces of invariant means.

o estimate the rotation of axes of coordinate system [O.sub.2][x.sub.2][y.sub.2] [z.sub.2] relative to the axes of stationary coordinate system [O.sub.1] [x.sub.1] [y.sub.1] [z.sub.1, it is formed a homogeneous

matrix transformations.

It should be mentioned that [E.sub.1] can be transformed to form (38) by proper

matrix transformations which will not change the structures of [B.sub.1] and [C.sub.1].

The notion of regularity for two dimensional

matrix transformations was presented by Silverman [40] and Toeplitz [41].

Characterisations of classes of

matrix transformations between sequence spaces constitute a wide, interesting and important field in both summability and operator theory.