%0 Journal Article
%T 一类线性变换的若干等价刻画<br>Some Equivalent Characterizations of a Class of Linear Transformations
%A 常学武
%A 郭巧萍
%A 黄谦
%J Pure Mathematics
%P 194-199
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/pm.2024.145176
%X 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。<br />
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.
%K 线性变换，最小多项式，特征多项式，特征值，几何重数，Frobenius矩阵，Jordan块<br>Linear Transformation
%K Minimal Polynomial
%K Characteristic Polynomial
%K Eigenvalue
%K Geometric Multiplicity
%K Frobenuius Matrix
%K Jordan Block
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=87579