可交换矩阵的一些性质

Some Properties of Commutative Matrices

研究了可交换矩阵特征向量的关系.证明了当方阵A,B可交换时,任取A的特征值存在B的特征值满足它们特征向量的交集非空.给出了在已知A的特征值、特征向量的前提下,求与A可交换矩阵特征值、特征向量的一种比较简单的方法,并举例说明了该方法的有效性.

The relationship between eigenvectors of two commutative matrices is studied. If A,B are commutative,then for any eigenvalue of A, there exists an eigenvalue of B, the intersection of their eigenvectors is non-empty. The eigenvalues and eigenvectors of A are given and a simple meth- od is obtained to calculate those of the matrices which are commutative to A. Also, some illustrating examples are presented to show the ellectiveness of the results.