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• W2001919076 abstract "In 1979, Campbell and Meyer proposed the problem of finding a formula for the Drazin inverse of a 2 × 2 matrix M=ABCD in terms of its various blocks, where the blocks A and D are required to be square matrices. Special cases of the problems have been studied. In particular, a representation of the Drazin inverse of M, denoted by MD, has recently been obtained under the assumptions that C(I − AAD)B = O and A(I − AAD)B = O together with the condition that the generalized Schur complement D − CADB be either nonsingular or zero. We derive an alternative representation for MD under the same assumptions, but with the condition on the Schur complement in the hypothesis replaced by the condition that R(CAAD)⊂N(B)∩N(D), where R(·) and N(·) are the range and null space of a matrix." @default.
• W2001919076 created "2016-06-24" @default.
• W2001919076 creator A5014988509 @default.
• W2001919076 creator A5070227245 @default.
• W2001919076 date "2007-06-01" @default.
• W2001919076 modified "2023-09-25" @default.
• W2001919076 title "A note on the representations for the Drazin inverse of 2×2 block matrices" @default.
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• W2001919076 doi "https://doi.org/10.1016/j.laa.2007.01.005" @default.
• W2001919076 hasPublicationYear "2007" @default.
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