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New representations of the group inverse of \(2 \times 2\) block matrices. (English) Zbl 1271.15001

Summary: This paper presents a full-rank factorization of a \(2 \times 2\) block matrix without any restriction concerning the group inverse. Applying this factorization, we obtain an explicit representation of the group inverse in terms of four individual blocks of the partitioned matrix without certain restriction. We also derive some important coincidence theorems, including the expressions of the group inverse with Banachiewicz-Schur forms.

MSC:

15A09 Theory of matrix inversion and generalized inverses
15A23 Factorization of matrices
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