Characterizations Of Normal Matrices,EP Matrices,k-Generalized Projection And Khypergeneralized Projection

This paper mainly studies the properties of normal matrix,EP-matrix,k-generalized projection,k-hypergeneralized projection,many of the properties of the former two special matrices are studied,I will consider the properties of them on the other hand,the content of each chapter arrange as follows:The first chapter introduces the research background,the research that we study by the people all over the world,the symbols and lemmas that need to be used in this paper.In the second chapter,based on the former gave the sufficient and necessary condition of the normal matrix by the ?-K-L of decomposition,some new characterizations of the normal matrix are given by AA*?A*A.that also used the ?-K-L of decomposition.In the third chapter,on the condition of the ?-K-L decomposition,the necessary and sufficient condition of EP-matrix is L=0.In this section,we use the ?-K-L decomposition to introduces some new nature of EP-matrix by using AA+?A+A and characterizes its properties by A(?)and A(?).In the fourth chapter,the properties of the four idempotent normal matrix and the four idempotent EP-matrix are applied to the k-generalized projection and the k-hypergeneralized projection.In the fifth chapter,some partial order of k-generalized projection,k-hypergeneralized projection are briefly introduced and prospect.