A Representation for the Drazin Inverse of Block Matrices with a Singular Generalized Schur ComplementApplied Mathematics and Computations
AbstractConsider a 2×22×2 block complex square matrix M=ABCD, where A and D are square matrices. Suppose that (I-AAD)B=O(I-AAD)B=O and C(I-AAD)=OC(I-AAD)=O, where ADAD is the Drazin inverse of A . The representations of the Drazin inverse MDMD have been studied in the case where the generalized Schur complement, S=A-CADBS=A-CADB, is either zero or nonsingular. In this paper, we develop a representation, under certain conditions, for MDMD when S is singular and group invertible. Moreover, this formula includes the case where S=OS=O or nonsingular. A numerical example is given to illustrate the result.
Citation InformationXiezhang Li. "A Representation for the Drazin Inverse of Block Matrices with a Singular Generalized Schur Complement" Applied Mathematics and Computations Vol. 217 Iss. 18 (2011) p. 7531 - 7536
Available at: http://works.bepress.com/xiezhang_li/11/