Hamilton-Cayley定理的证明  

Several Proofs of Hamilton-Cayley Theorem

作　　者：陈璞[1] 刘运谋 CHEN Pu;LIU Yun-mou(Department of Mechanics,Peking University,Beijing 100871,China)

机构地区：[1]北京大学工学院力学与工程科学系

出　　处：《大学数学》2019年第6期48-57,共10页College Mathematics

基　　金：北京大学力学基地科研训练及科研能力提高项目(J13100100);国家自然科学基金资助项目(11472014,11521202)

摘　　要：Hamilton-Cayley定理是《高等代数》中最基本与深刻的定理之一,也是其中课程中知识与方法的集散点之一.它的证明方式涉及几乎所有《高等代数》的知识,引伸出的涵义也多种多样.文中回顾了Cayley,Hamilton与Frobenius的三种原始证明,并梳理了目前《高等代数》教材中的数种证明,最后讨论不同证明之间的联系.The beautiful Hamilton-Cayley theorem is one of the most primary and profound theorems in linear algebra.It is a concentration of approaches and knowledgements in teaching.Its various proofs cover almost all contents of linear algebra with colorful extensions and connotations.This article starts with the original proofs contributed by Cayley,Hamilton and Frobenius,then concludes several kinds of proofs in modern textbooks.Finally,connections between various proofs are discussed in different aspects.

关 键 词：Hamilton-Cayley定理 伴随矩阵 最小多项式 标准形 

分 类 号：O177.5[理学—数学]