Geodesic
A Singular Inverse of a Matrix by Rank Annihilation
Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 1-4

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Edelblute [1] has given a method of finding an inverse of a nonsingular matrix by rank annihilation. The purpose of this paper is to show that the method can be extended in the case of a singular matrix. This method will produce a singular inverse satisfying condition (3) of Penrose [3]. 
Ahsanullah, M.; Rahman, M. A Singular Inverse of a Matrix by Rank Annihilation. Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 1-4. doi: 10.4153/CMB-1973-001-4
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