广义特征向量与过渡矩阵

The GeneraLized Eigenvector and the Transition Matrix

介绍了矩阵A的广义特征向量及利用A的特征向量ζ通过方程（A-λE）x=ζ逐次由秩数低的广义特征向量求出A的秩数高的广义特征向量；首次证明了矩阵A的按此法求得的这些广义特征向量是线性无关的；首次证明了n阶矩阵恰有n个线性无关的广义特征向量；首次给出了用这些广义特征向量为列来构造过渡矩阵P，使P^-1AP为A的约当标准形的方法。

This articLe introduces method to obtain generaLized eigenvectors. The Linear independence of aLL generaLized eigenvectors was proved. It is proved that -order matrix just have pieces of the Linear independent generaLized eigenvectors. Making transition matrix with these Linear independent generaLized eigenvectors was introduced.