Representations of the Drazin inverse on solution of a class singular differential equations
Changjiang Bu, Kuize Zhang, Jiemei Zhao · Linear and Multilinear Algebra · 2011
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.