ON BORDERING OF REGULAR MATRICES

Necessary and sufficient conditions are given for a commutative ring R to be a ring over which every regular matrix can be completed to an i nvertible matrix of a particular size by bordering. Such rings are pre cisely the projective free rings. Also, over such rings every regular matrix has a rank factorization. Using the bordering technique, we giv e an interesting method of computing miners of a reflexive g-inverse G of a regular matrix A when I - AG and I - GA have rank factorizations .