Abstract
The sign pattern of a real matrix A, denoted by sgnA, 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 sgnB = sgnA. 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, XAX = X and AX = XA, where k is the Drazin index of A. We say that A has signed Drazin inverse if \(\operatorname{sgn} {\tilde A^d} = \operatorname{sgn} {A^d}\) for any \(\tilde A \in Q(A)\), where A d denotes the Drazin inverse of A. In this paper, we give necessary conditions for some block triangular matrices to have signed Drazin inverse.
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The research is supported by the National Natural Science Foundation of China under grant 11371109, and the Fundamental Research Funds for the Central Universities.
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Bu, C., Wang, W., Zhou, J. et al. On block triangular matrices with signed Drazin inverse. Czech Math J 64, 883–892 (2014). https://doi.org/10.1007/s10587-014-0141-6
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DOI: https://doi.org/10.1007/s10587-014-0141-6