The Inverse,group Inverse,core Inverse,and Generalized Core-EP Inverse Of The Combinations Of Two Projectors

Projection operator and the generalized inverse of the matrix are important research topics in the generalized inverse theory. In recent years, the Chinese and foreign scholars have made a lot about generalized inverse of the linear combination of all kinds of special matrix. This paper mainly studies the characteristics of the generalized inverse of the combinations of two idempotent matrices by the method of space decomposition of matrix and MCS decomposition. Contents are arranged as following:The first chapter mainly introduces the necessary symbols,definitions and main arrangements.The second chapter firstly introduces the sufficient and necessary condition for the existence of group inverse of two idempotent operators,and then the expressions of inverse and group inverse are given in different conditions.The third chapter firstly introduces the basic concept of the Core inverse and lemmas,and the expressions of Core inverse of combinations of two idempotent operators are given. Further, this paper introduces Core-EP generalized inverse.