The Generalized Inverses Of The Combination Of Two Idempotent Matrices

Projection operator and the generalized inverse of the matrix are important research topics in the matrix theory.In recent years,the Chinese and foreign scholars have made a lot about generalized inverse of the combination of many kinds of special matrices.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 M-C-S decomposition.Contents are arranged as following:The first chapter,we simply introduce the generalized inverse matrix,the research background,meaning at home and abroad symbols and the necessary symbols.The second chapter,we firstly introduce the sufficient and necessary conditions for the existence of inverse of the combination of two idempotent operators in different conditions,then give the formulas of the inverses.The third chapter,we firstly introduce the definition of the Group inverse and lemmas,then study the Group inverses of the combination of two idempotent operators are given.The forth chapter,we firstly introduce the definition of the Core inverse and lemmas,then study the Core inverses of the combination of two idempotent operators are given.