Abstract: From the point of view of linear transformation, the scattering transformation and its different scattering matrices are studied in this paper. The different scattering matrices in different cartesian coordinates and their changes are presented. Then, it is proved that Sinclair scattering matrix is based on a cross process in two different coordinates, i. e. , it is a non-common-basis-state matrix of the scattering transformation, it can not determine the eigenvalue polynomial of this scattering transformation. In the meantime, it shows clearly the inverse process of getting the eigenvalue polynomial from converting the Sinclair scattering matrix into the generalized scattering matrix.