Two Methods for Computing the Drazin Inverse through Elementary Row Operations

Abstract

In this paper, for a matrix $A\in C^{n\times n}$ with $Ind(A)=k$, we first
construct two bordered matrices based on [32], which gave a method for computing the null space
of $A^k$ by applying elementary row operations on the pair $ \left(\begin{array}{cc}
A & I
\end{array}\right)$. Then two new methods for computing the Drazin inverse $A^d$ are presented based on elementary row
operations on the above tow partitioned matrices. In the end, an example is presented to demonstrate the two new algorithms.