线性空间直和分解定理的推广及应用

摘要

In this paper,theorem of direct sum decomposition of a linear space in advanced Algebra is generalized.For any Annihilating polynomial f（x） of a linear transformation A,if f（x） is a product of finite mutually prime polynomials,linear space V could be deco%把高等代数中线性空间的直和分解定理推广到一般情形.对于n维线性空间V上线性变换A的任一个化零多项式f（x）,若f（x）为若干个两两互素的多项式的乘积,则线性空间V可以相应地分解成有限个A的不变子空间的直和.一些应用实例被给出.