THE EXPLICIT EXPRESSION OF THE DRAZIN INVERSE OF SUMS OF TWO MATRICES AND ITS APPLICATION

Abstract

In this paper, we give explicit expressions of (P \(\pm\) Q)_d of two matrices P and Q, in terms of P, Q, P_d and Q_d, under the condition that PQ = P², and apply the result to finding an explicit representation for the Drazin inverse of a 2 x 2 block matrix

\(\begin{bmatrix} A & B \\ C & D \\ \end{bmatrix}\) under some conditions.