亏损矩阵特征子空间的分解与若当链一般形式

The decomposition of the eigenspace of the defective matrix and the general form of Jordan chain

对于复数域上的方阵 A,用 (λi I - A) j的列空间及其一个余子空间与特征子空间的交可以找到具有相同长度的若当链首元中心 ,从而得到求若当链的一种方法 .特征子空间可以分解成这些中心的直和 .再根据若当链上不同位置的向量的运算关系 。

The center of Jordan chains with the same length can be found by the intersection between the column space of (λ-iI-A)+j and its co-space and the eigenspace, and a method of obtaining Jordan chain is got. The eigenspace can be broken down into the direct sum of the center. According to the operating relation between vectors on different positions of Jordan chains, the general form of Jordan chain can be given.