矩阵的最小多项式及其应用

Minimum Polynomial of Matrix and Its Application

基于最小多项式的理论,介绍了用特征多项式求最小多项式的方法,归纳了最小多项式在简化任意矩阵多项式、求线性空间的维数和基、解矩阵方程,以及判断矩阵对角化这四方面的应用。

Based on the theory of minimum polynomials, this paper introduces the method of finding the minimum polynomials with characteristic polynomials, and sums up the application of minimum polynomials in simplifying arbitrary matrix polynomials, finding dimensions and bases of linear spaces, solving matrix equations, and diagonalizing judgment matrices.