复矩阵的Jordan标准形的存在性的新证明  

A New Proof of the Existence of Jordan Canonical Forms of a Complex Matrix

作　　者：孙玉峰[1] 谢祥云[1] 

机构地区：[1]五邑大学,数学物理系

出　　处：《五邑大学学报（自然科学版）》2007年第1期24-28,共5页Journal of Wuyi University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10341002);广东省自然科学基金资助项目(0501332).

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．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.

关 键 词：JORDAN标准形 复矩阵 模 

分 类 号：O152.7[理学—数学]