关于Cayley-Hamilton定理的连续论证法  

Consecutively demonstration method of the Cayley-Hamilton theorem

作　　者：邓勇[1] 

机构地区：[1]喀什师范学院数学系,新疆喀什844006

出　　处：《南阳师范学院学报》2014年第12期1-3,共3页Journal of Nanyang Normal University

基　　金：新疆维吾尔自治区高校科研计划重点项目(XJEDU2008131)

摘　　要：Cayley-Hamilton定理是线性代数中的一个重要结论.对该定理从不同角度入手的证明也多种多样.为丰富线性代数的这部分理论,首先对有限维向量空间某些结果的论证进行了改进,然后利用矩阵数值分析的连续论证法,给出了Cayley-Hamilton定理的另一种新证明.Cayley-Hamilton theorem is an important theorem in linear algebra. However, there were various methods to prove the theorem from different angles. To enrich the theory of linear algebra, first of all, the proof of some conclusions were improved in the finite dimensional vector Space, and then a new simple proof was given on the Cayley-Hamihon theorem by continuous argument method for the numerical analysis.

关 键 词：矩阵三角化 向量空间 CAYLEY-HAMILTON定理 连续论证法 FROBENIUS范数 

分 类 号：O151.22[理学—数学]