Abstract
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 invertible matrix of a particular size by bordering. Such rings are precisely the projective free rings. Also, over such rings every regular matrix has a rank factorization. Using the bordering technique, we give an interesting method of computing minors of a reflexive g-inverse G of a regular matrix A when I − AG and I − GA have rank factorizations.
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