New representations of the Moore–Penrose inverse of 2×2 block matrices

This paper presents a full rank factorization of a 2×2 block matrix without any restriction. Applying this factorization, we obtain an explicit representation of the Moore–Penrose inverse in terms of four individual blocks of the partitioned matrix, which simplifies results of Hung and Markham (1975) [12], , and Miao (1991) [16]. We also derive some important coincidence theorems, including in the expressions of the Moore–Penrose inverse of a sum of matrices. All these results extend earlier works by various authors.