Representations For The Drazin Inverse Of Block Matrices

In this thesis, we focus on the explicit representations for the Drazin inverse of antitriangular block matrices and the generalized Drazin inverse of operator block matrices:In chapter 1, we systematically summarize the development course of generalized inverse and its development status, and then we show some research achievements of the Drazin inverse of block matrices and the generalized Drazin inverse of operator block matrices. At last,we briefly described the main work content.In chapter 2, we give five theorems and let the anti-triangular block matrices split into two matrices, and then we present the Drazin inverses of anti-triangular block matrices under the eight conditions.In chapter 3, we firstly give some basic definitions and theorems, and we show the generalized Drazin inverse for the sum of the two elements under the three conditions.