幂法求解实非对称矩阵特征值问题的注记

Notes on Solving Eigenvectors of Real Asymmetical Matrix with Power Method

本文在特征值及右特征向量均为已知的条件下,提出一种直接求解左特征向量的方法。另外,还证明了特征值及特征向量的一个重要定理。如果矩阵最后一个特征值为实数时,利用这一定理可直接求解该特征对。

This paper presents a direct solution to the left eigenvector of the asymmetrical matrix under the condition that the eigenvalue and the right eigenvector are known. In additon, an important theorem of the eigenvalues and the eigenvectors is demonstrated. The last eigenvalue and the corresponding left and right eigenvectors can be solved directly by applying this theorem if the Iast eigenvalue is real.