Explicit formulae for the Drazin inverse of the sum of two matrices

Abstract In this article, we construct a new explicit formula for the Drazin inverse of a sum of two matrices P, Q ∈ ℂ n×n under conditions weaker than those used in some recent papers, and modify an invalid formula in [Dopazo et al.: Block representations for the Drazin inverse of anti-triangular matrices , Filomat 30 (2016), 3897–3906]. Furthermore, we apply our results to obtain some new representations for the Drazin inverse of a 2 × 2 block matrix. Some numerical examples are given to illustrate our results.