The Study Of The Intertwining Relationship Between Some Structed Matrices

With the rich of matrix theory and the apply more widely, the study of the connection between matrices become an important research topic in matrix and operator theory. This paper focus on the study of the operator of matrices in different basis, at the same time we also use operator method to study the intertwining relation-ship between some structed matrices.The first chapter described the background and the main work of this paper. The second chapter recall the necessary basic knowledge, focuses on the basis of operators and basis. The third chapter, firstly given some special matrices and operator concepts and basic properties, and then based on the operator we given some new matrices of operator representation, finally, we use the method of the given operator give equival-ent representation about some already existing results. Section1of Chapter IV firstly give intertwining relationship of classical Bezout matrix, and then give a further study about intertwining relationship of Toeplitz-Bezout matrix on the basis of it. In Section2, using a similar method to the Section1of the intertwining relationship of Hankel matrix, and then give a further study about intertwining relationship of Toeplitz-Hankel matrix on the basis of it. Section3simply give and prove intertwining relationship of some new special matrix.