On block triangular matrices with signed Drazin inverse

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 for any , 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.