Expressions for the Drazin inverse of a modied matrix

Lazar Stojkovic, Dijana Mosic


We present some new expressions for the Drazin inverse of a modified matrix $A −
CD^DB$ in terms of the Drazin inverse of A and its generalized Shur’s complement
$D − BA^DC$ under weaker conditions. Some results in recent literature are unified and
generalized, and most importantly, we obtain new expressions of generalized Sherman-
Morrison-Woodbury formula under weaker restrictions.


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