Differentiation of the Drazin Inverse
Stephen L. Campbell · SIAM Journal on Applied Mathematics · 1976
Suppose that A is an $n \times n$ matrix of differentiable functions. Suppose that $A^D $ is defined as $A^D (t) = [ {A(t)} ]^D $ , where $[ {A(t)} ]^D $ is the Drazin inverse of the $n \times n$ matrix $A(t)$. A formula is derived for the derivative of $A^D $ in terms of A, $A^D $ and the derivative of A. The conditions under which $A^D $ is differentiable are discussed.