The present note is perhaps of theoretical interest only but is intended to exhibit in somewhat general perspective the classical elimination methods for inverting matrices, and a seemingly different one proposed recently by Hestenes (1953, 1957). These will be seen to be special cases of a general class of possible methods, although possible new variants may or may not turn out to possess practical advantages. The description of the class as a whole will be based upon the following: LEMMA. Let P be a nonsingular matrix of order n, and let Q be a matrix of rank n r at most. Then if P Q has rank r + 1 at least, there exist column vectors u and v and a scalar ar such that I o-uv is nonsingular and
 Iterative computational methods , 1955 .