Characterizations And Properties Of Bott-Duffin Inverse,co-BD Matrices And BD Matrices

In this paper,we mainly discuss the characterization and properties of Bott Duffin inverse,co BD matrix and BD matrix The research contents of this paper are as follows:The first chapter mainly introduces the background and significance of this topic,as well as the research status of the topic at home and abroad.At the same time,we also introduce the relevant notations,definitions and some important lemmas needed in this paperIn chapter 2,we give some new characterizations and properties of the Bottom-Duffin inverse.Some of the results available in the literature are recaptured in a more general form.Moreover,the relationship between the Bottom Duffin inverse and other generalized inverses are presented.In chapter 3,we give the characterizations and properties of co-BD matrices by using rank equality and subspace operations.Further,we discuss the equivalences of the nonsingularity of AA_（L）^（-1）+A_（L）^（-1）A and I_n-A(A_（L）^（-1）)²A.The representations of the inverses of AA_（L）^（-1）-A_（L）^（-1）A,AA_（L）^（-1）+A_（L）^（-1）A and I_n-A(A_（L）^（-1）)²A are presented.In chapter 4,we show the characterizations of BD matrices,and consider the e-quivalences of A^*A_（L）^（-1）=A_（L）^（-1）A^*.Moreover,consider the relationship between BD matrices and A^*A_（L）^（-1）=A_（L）^（-1）A^*.Chapter 5 summarizes the main work and innovation of this paper,and gives the future research direction of this topic.