In this paper the following sequence space is presented. Let [t] be a positive double sequence and define the sequence space Omega '' (t) = {complex sequences x : x(k,l) = O(t(k,l))}. The set of geometrically dominated double sequences is defined as G ''-U(r,s is an element of(0,1))G(r,s) where G (r,s) - {complex sequences x : x(k,l) = O(r(k)s(l))} for each r,s in the interval (0, 1). Using this definition, four dimensional matrix characterizations of l(infinity,infinity), c '', and c(0)'' into G '' and into Omega ''(t) are presented. In addition to these definitions and characterizations it should be noted that this ensure a rate of converges of at least as fast as [t]. Other natural implications will also be presented.