Let X and Y be Banach spaces and L(X,Y) the space of all continuous lincar operators from X into Y. In this paper, we give characterizations of infinite matrices whose entries are in L(X,Y) mapping from the X-valued sequence spaces ¤ ¥ (X,p), co(X,p), c(X,p) and l(X,p) into the Y-valued sequence spaces co(Y,q) and c(Y,q) where p=(pk) and q = (qk) are bounded sequences of positive real numbers.