The Properties Core-EP Inverse Of Matrix

The main aim of this paper is to investigate the properties Core-EP inverse of matrix.The thesis is divided into four chapters:In chapter 1,we introduce the background,the present situation and the development trend of research on generalized inverse.We also introduce the necessary preliminaries.In chapter 2,we give the necessary and sufficient conditions of A{1~k}inverse,investigate the necessary and sufficient conditions of Core-EP inverse when the A{1~k}inverse exists,we established the representation of limiting and integral for Core-EP inverse by the decomposi-tion of Core-EP of the matrix.In chapter 3,the classical Cayley-Hamilton theorem is generalized to the Core-EP inverse matrix and DMP inverse matrix.In chapter 4,two explicit representations for the Drazin inverse of a 2×2 block complex matrix are presented and we also present several representations for the Drazin inverse of M under some conditions.