Some Properties Of K-generalized Projectors And K-hypergeneralized Projectors

In this paper,by the Σ-K-L decomposition we mainly study the properties and characterizations of k-generalized projectors(Ak=Ab)and k-hypergeneralized projectors(Ak-A+).Also,utilizing the matrix decomposition we study the invertibility and MP-inverse of combinations of commuting k-generalized and k-hypergeneralized projectors.The content of this paper is organized as followsIn the first chapter,we introduce the background of the selected topic,the resear-ch status and the symbols required in the articleIn the second chapter,using the properties of some special matrices(such as normal,EP,weak-EP,m-EP,m-normal and k-potent matrices,etc.),by the Σ-K-L decomposition,we give several further properties of k-generalized and k-hypergeneralized projectorsIn the third chapter,we present necessary and sufficient conditions for the invert-Ibility and representations for the MP-inverse of combinations of commuting k-gen-eralized and k-hypergeneralized projectors by the matrix decomposition.Also,we give the formula of the invertibility under certain conditions.