关于与给定矩阵可交换的矩阵的多项式表示

摘要

[1-] obtained： if there is not the Jordan block corresponding to the scalar matrix in the Jordan canonical form of the matrix A, then the necessary and sufficient condition of AB = BA is that B can be （n- 1 ）-order polynomial about A. In the paper, we pointed the conclusion is wrong. On the basis of the previously related literatures, we derive ten equivalent characterizations that the matrix B being changeable with given matrix A is the polynomial about A.%文[1]得到：若矩阵A的Jordan标准形中没有纯量矩阵的Jordan块,那么AB=BA的充要条件为B可以化为A的n-1次多项式.本文指出这个结论是错误的.在已有相关文献的基础上,得到了与给定矩阵A可交换的矩阵B是A的多项式的十个等价刻划.