The recursive projection algorithm (RPA), derived from the vector Sylv
ester identity, has a connection with the recursive interpolation algo
rithm (RIA). These algorithms have many applications and connections w
ith some other methods used in various areas of numerical analysis. Th
e aim of this paper is to study some properties of these algorithms. W
e use properties of projectors, a matrix implementation and the Schur
complement extended to the vector case, to give a result about their f
inite termination.