Abstract
In 1983, Campbell proposed a problem to find an explicit representation of the Drazin inverse for the block matrix with E and F square in terms of E and F according to the research on singular differential equations. In this article, we give the representations of the Drazin inverse for
with E and F square under the condition that EF = FE and the Drazin inverse for
with E square under the condition that EFG = FGE, and then give some representations under some other conditions, so as to solve the problem partially and to get some extra results.
Acknowledgements
Supported by Natural Science Foundation of the Heilongjiang Province, No. 159110120002.