The classical Cesaro sequence space and its algebraic dual and related matrix transformations
were introduced and studied by various authors like Shiue , Leibowitz , Lim , Khan and Khan ,, Khan and Rahman , Johnson and Mohapatra , Rahman and Karim , 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  and Toeplitz .
Characterisations of classes of matrix transformations
between sequence spaces constitute a wide, interesting and important field in both summability and operator theory.