矩阵标准形的应用  

Applications of Standard Form for Matrix

作　　者：张姗梅[1] 刘耀军[1] 

机构地区：[1]太原师范学院,山西晋中030619

出　　处：《忻州师范学院学报》2016年第2期8-12,共5页Journal of Xinzhou Teachers University

基　　金：山西省高等学校教学改革项目(J2015137)

摘　　要：矩阵的等价、相似与合同是矩阵之间的三种重要的等价关系,按照这三种等价关系可将矩阵作相应的分类,由此产生了矩阵的各种标准形,每种标准形都是该等价类的最简形式。当面临的问题复杂、抽象,感到无从下手之时,可尝试先对标准形解决,再根据矩阵的一些在等价、相似、合同关系下不变的性质,比如相似矩阵有相同的特征值,将一般矩阵问题转化成标准形问题处理。通过例子说明:应当运用化归思想,借助矩阵的相应标准形可以解决有关矩阵的问题。The equivalence,similarity and contract are three important equivalence relations for matrices,and the matrices are classified according to these relations. The standard form of matrix is the simplest delegate for its equivalent class. When face with the complex,abstract and difficult matrix problems,it can be considered for their standard form first then solved the general case. The principal is that there are some invariant properties for these relations,such as similar matrices have same eigenvalue. Examples are given to illustrate the method how to solve matrix problem by transforming the general case to their corresponding standard form.

关 键 词：矩阵 标准形 等价 相似 合同 若尔当块 

分 类 号：O151.21[理学—数学]