一类线性变换的若干等价刻画

Some Equivalent Characterizations of a Class of Linear Transformations

摘要: 众所周知，有限维线性空间上的线性变换的最小多项式是其特征多项式的因式。本文给出最小多项式恰好等于特征多项式的线性变换的若干等价刻画。

Abstract: It is well known that the minimum polynomial of a linear transformation of a finite dimensional linear space is a factor of its characteristic polynomial. This article provides several equivalent characterizations of linear transformations whose minimum polynomial happens to equal to the characteristic polynomial.