矩阵A的中心化子可表成A的方阵多项式的充要条件

A Necessary and Sufficient Condition of Matrices Polynomial Representations for Centralizers of Matrices

n阶矩阵A的中心化子C(A) ={B∈Pn×n|AB =BA} ,P[A] ={f(A)∈Pn×n|f(x)∈P[x] } 本文给出了C(A) =P[A] 。

Suppose C(A)=｛B∈p n×n ｜AB=BA｝ matrix A with order n, and P[A]=｛f(A)∈p n×n ｜f(x)∈P[x]｝ A necessary and sufficient condition of C(A)=P[x] is given in this paper