可逆可对角化矩阵最小多项式的行列式表示法

摘要

用同构映射与初等变换研究矩阵的最小多项式问题,提出一种新的求矩阵最小多项式的简便方法.进一步地,对可逆的可对角化矩阵,用行列式建立其最小多项式的表达公式.%Applying the properties of the isomorphism and elementary transformations, a simple and efficient algorithm for calculating the minimal polynomial of matrices was provided. Moreover, the explicit formula of the minimal polynomial of invertible and diagonalizable matrix was obtained by means of determinants.