关于散射变换的特征问题

Eigenvalue Problems on the Scattering Transformation

本文从线性变换的角度出发,讨论了散射变换及其相关的散射矩阵.在不同坐标系下,给出了散射矩阵的各种表达形式及其转换关系.在此基础上指出了Sinclair双站散射矩阵是散射变换在两个不同坐标系下交叉构成的,是散射变换的非自同态矩阵,它不能直接确定散射变换的特征多项式.文中同时指出了由Sinclair散射矩阵还原目标散射矩阵,从而获得特征多项式的逆变换过程.

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.