The Index and the Drazin Inverse of Block Triangular Matrices

Bounds for the index of block triangular matrices are given in terms of the indices of the diagonal blocks. For a matrix of the form \[ M = \left[ {\begin{array}{*{20}c} A &\vline & B \\ \hline 0 &\vline & C \\ \end{array} } \right] \] where A and C are square, an explicit formula for the Drazin inverse, $M^D $, of M is given which is a function of $A,B,C,A^D $ and $C^D $ only.