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On block triangular matrices with signed Drazin inverse

Changjiang BuWenzhe WangJiang ZhouLizhu Sun — 2014

Czechoslovak Mathematical Journal

The sign pattern of a real matrix A , denoted by sgn A , is the ( + , - , 0 ) -matrix obtained from A by replacing each entry by its sign. Let 𝒬 ( A ) denote the set of all real matrices B such that sgn B = sgn A . For a square real matrix A , the Drazin inverse of A is the unique real matrix X such that A k + 1 X = A k , X A X = X and A X = X A , where k is the Drazin index of A . We say that A has signed Drazin inverse if sgn A ˜ d = sgn A d for any A ˜ 𝒬 ( A ) , where A d denotes the Drazin inverse of A . In this paper, we give necessary conditions for some block triangular matrices to have signed...

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