【摘要】 介绍了关于模的基本概念,证明了具有有限生成元集、公共最大阶数的Z-模、C[x]-模的唯一分解定理．然后把它应用到一个具体的C[x]-模V,其中V是n维线性空间, C[x]×V到V的映射由V中的一个线性变换T定义,从而得到V的一个唯一分解,再结合线性代数有关知识给出V的一组基,T在这组基下的变换矩阵恰为T的Jordan标准形．更多还原

【Abstract】 In this paper we first introduce some notations about module and prove that Z-modules and C[x] -modules, which have finitely many generators and whose elements have common largest order, can be uniquely factorized. Then we apply it to a C[x] -module V , where V is a n-dimensional vector space and the operator from C[x]×V to V is defined by a linear transformation T of V , then we get a unique factorization of V and a right basis under which the transformation matrix of T is T ’s Jordan canonical form. In other words, we prove the theory of the existence of the Jordan canonical form of a complex matrix.更多还原