A Characterization and Representation of the Drazin Inverse
SIAM Journal on Matrix Analysis and Applications
Index splitting for the Drazin inverse and the singular linear system
Applied Mathematics and Computation
On the perturbation of the group inverse and oblique projection
Applied Mathematics and Computation
Successive matrix squaring algorithm for computing the Drazin inverse
Applied Mathematics and Computation
| Hi-index | 0.48 |
For a square matrix A of index 1, the block-rank equation rank[A/C B/X] = rank(A) is studied. Geometrical conditions are given to characterize the solution of this equation. Further, all matrices B and C are described for the solution X = A#, where A# is the group inverse of A. In addition, we extend these results to reflexive generalized inverses. This contributes to a result recently obtained by Wei [SIAM J. Matrix Anal. Appl. 17 (1996) 744] and it is a generalization of a result by Groß [Lin. Alg. Appl. 289 (1999) 127].