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A note on the representations for the Drazin inverse of $2 \times 2$ block matrices. (English) Zbl 1121.15008
Given a matrix $M = \left[ {\matrix A & B \\ C & D \\ \endmatrix } \right]$, where $A \in {\Bbb C}^{m \times m} $ and $D \in {\Bbb C}^{n \times n}$, a new formula for the Drazin inverse $M^D$ is derived under the assumptions that: $A(I - AA^D)B = 0, C(I - AA^D)B = 0, BCAA^D = 0, DCAA^D = 0$.

15A09Matrix inversion, generalized inverses
Full Text: DOI
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