A Representation of the Drazin Inverse for the Sum of Two Matrices and the Anti-Triangular Block Matrices

Abstract

In this paper, a new formula for the Drazin inverse for the Sum of Two Matrices is given under conditions weaker than those used in some current literature. Further, we apply our results to obtain new representations for the Drazin inverse of an anti-triangular block matrix under some conditions, which also extend some existing results.

Keywords

• Drazin inverse
• index
• anti-triangular block matrix
• additive formula