Some block matrices with signed Drazin inverses

Abstract The sign pattern of a real matrix M is the ( 0 , 1 , - 1 ) -matrix obtained from M by replacing each entry by its sign. Let Q ( M ) be the set of real matrices with the same sign pattern as M . For any M ∼ ∈ Q ( M ) , if the Drazin inverses of M and M ∼ have the same sign pattern, then M is said to have signed Drazin inverse. In this paper, we give a complete characterization for a class of anti-triangular matrices with signed Drazin inverse, and present a complete characterization for sign symmetric bipartite matrices with signed Drazin inverse.

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