Group inverse for the block matrices with an invertible subblock

Group invertible block matrices

“…Next, we give the existence and representation for the group inverse of a block matrix which generalizes a result of [3]. …”

“…Campbell and Meyer [9] proposed an open problem to find an explicit representation for the Drazin Bu et al [3] gave the existence and the representations for the group inverse of M, when A is invertible and the group inverse of the Schur complement S = D − CA −1 B exists. Deng and Wei [13] showed the existence and the representations for the group inverse of M when the group inverse of…”

A note on the group inverse of some 2 × 2 block matrices over skew fields

“…For example, it can be applied to solve constrained optimization problems (KKT Linear Systems), and also can be used in finding the solution of differential equations (see [20-22]). About this open problem, there have been some results under some certain conditions (see [10][11][12][13][14][15][16][17][18][23][24][25]). Specially, in papers [15,16,18,24], the existence and the representations of the group inverse for the following block matrices are researched: [24]); [15]);…”

A note on block representations of the group inverse of Laplacian matrices

“…For a matrix B, let B + denote the Moore-Penrose inverse of B. Some representations for the group inverse of block matrices (operators) are given in [2][3][4][5][6][7][8]11,12,14,16,17,28]. More details for the theory of generalized inverse can be found in [9].…”