分块三角矩阵的一类特征子空间

The Eigenspace of Block Triangular Matrix

本文讨论分块三角矩阵的一类特征子空间的结构，得到的结论是：如果矩阵Ｃ有一个特征根等于非负不可约矩阵Ａ的Ｐｅｒｒｏｎ根λＡ，那么，分块三角矩阵的相应于特征根λＡ的特征子空间可以用矩阵Ａ、Ｃ的相应于λＡ的特征子空间来刻划。

In this article,we investigate the structure of the eigenspace of a block triangular matrix We have obtained the following main result. If matrix C has a eigenvalue which is equal to λA,the Person'root of irreducible nonnegative matrix A,then the eigenspace of block triangular matrix, which correspond to eigenvalue λA, can be described by the eigenspace of matrix A and matrix C,which correspond to eigenvalue λA.