Research On The Bezoutian With Respect To A Jacobson Chain

In this paper some properties of classical Bezout matrix are characterized. In the first. The proof based on the operator approach are given and some other properties are discussed when the Bezout matrix under the general polynomial basic in the second chapter. The Bezoutian with respect to a Jacobson chain over an arbitrary field is introduced in Chapter 3. We mainly investigate the Barnett-type formula, intertwining with a hypercompanion matrix, and the diagonal reduction via the q-adic Vandermonde matrix for such matrices. The connection with the resultant matrix with respect to a Jacobson chain basis are discussed.Finally, the basic properties of Bezout matrix on an arbitrary field for using an operator method are discussed.