基于矩阵的特征多项式与最小多项式相关的探讨

Based on the Characteristic Polynomial of Matrix and the Minimum Polynomial Related Discussion

特征多项式是多项式和线性代数联系的纽带,是高等代数学习中重点和难点,它与最小多项式的结合又常常成为数学系硕士研究生入学考试的难点和焦点。本文从矩阵的特征多项式与最小多项式的定义出发,基于它们的最基本性质,对两者之间的关系进行了分析探讨并得到了一些有用结论。

Characteristic polynomial is the link between polynomial and linear algebra,is the emphasis and difficulty in higher algebra.It combined with the minimal polynomial often become the difficulties and focus in mathematics graduate entrance examination.Starting from the characteristic polynomial of matrix and the definition of minimal polynomial based on their basic properties,this paper analyzes the relationship between them and draws some useful conclusions.