SupposeXandYare FK spaces in which ϕ the span of the coordinate vectors (en) is dense. LetL(X,Y)denote the space of all matrices of the formEi(T(ej))asTranges over all continuous linear operators fromXintoY; hereeirepresents theithcoordinate vector andEirepresents theithcoordinate functional. LetM(L(X, Y))denote the space of all matricesBsuch that(B(i,j)A(i,j))is inL(X,Y)wheneverAis inL(X,Y).In this paper we shall show how the summability properties ofXandYdetermine the extent ofM(L(X,Y))and conversely how the extent ofM(L(X,Y))determines the summability properties of bothXandY.