方阵A的全体多项式所成线性空间的一个结论

A Conclusion on the Linear Space of All Polynomials of Square Matrix A

多项式是代数学中最基本的对象,文章根据方阵的运算和线性空间的一些基本定义和性质,以及方阵A的最小多项式的基本性质,给出了关于方阵A的全体多项式所成线性空间的维数的一个结论,是最小多项式的又一应用。

Polynomial is the most basic objects in algebra. In this paper, according to the operations of square matrix A and some basic definitions and properties of linear space, as well as the basic properties of the minimum polynomials associated with square matrix A, we present a conclusion concerning on the dimension of the linear space consisting of the set of polynomials associated with square matrix, which can be viewed as an application of minimum polynomials.